quantization and dynamisation of trace poisson brackets the quantization problem for the trace bracket algebra derived from double poisson brackets is discussed we obtain a generalization of the boundary ybe or so called abcd algebra for the quantization of quadratic trace brackets a dynamical deformation is proposed on the lines of gervais neveu felder dynamical quantum algebras

matching rota baxter algebras matching dendriform algebras and matching pre lie algebras abstract we introduce the notion of a matching rota baxter algebra motivated by the recent work on multiple pre lie algebras arising from the study of algebraic renormalization of regularity structures 10 19 this notion is also related to iterated integrals with multiple kernels and solutions of the associative polarized yang baxter equation generalizing the natural connection of rota baxter algebras with dendriform algebras to matching rota baxter algebras we obtain the notion of matching dendriform algebras as in the classical case of one operation matching rota baxter algebras and matching dendriform algebras are related to matching pre lie algebras which coincide with the aforementioned multiple pre lie algebras more general notions and results on matching tridendriform algebras and matching postlie algebras are also obtained

new generalized simple lie algebras of cartan type over a field with characteristic 0 abstract we construct four new series of generalized simple lie algebras of cartan type using the mixtures of grading operators and down grading operators our results in this paper are further generalizations of those in osborn s work j algebra 185 1996 820 835

the classification of novikov algebras in low dimensions novikov algebras were introduced in connection with the poisson brackets of hydrodynamic type and hamiltonian operators in the formal variational calculus for further our understanding and physical applications we give a classification of novikov algebras in dimensions two and three in this paper

on the central extensions of poisson brackets of hydrodynamic type poisson brackets of hydrodynamic type were introduced to construct a theory of conservation system of hydrodynamic type they lead to the algebraic and differentially geometrical theory of local translationally invariant lie algebras of first order frobenius type algebras and novikov algebras one of the main ways to construct new examples of these algebras and their corresponding poisson brackets is through the central extensions in balinskii a a and novikov s p 1985 sov math dokl 32 228 31 there is a general theory of the central extensions in this paper we give a further detailed study of two non trivial types of novikov algebras which directly decide an important kind of central extension of the poisson brackets we find that the novikov algebras in the case 3 are in the case 0 and these two cases coincide in dimension 3 moreover they also coincide for the transitive cases in dimension 4

noncommutative poisson bialgebras abstract in this paper we introduce the notion of a noncommutative poisson bialgebra and establish the equivalence between matched pairs manin triples and noncommutative poisson bialgebras using quasi representations and the corresponding cohomology theory of noncommutative poisson algebras we study coboundary noncommutative poisson bialgebras which leads to the introduction of the poisson yang baxter equation a skew symmetric solution of the poisson yang baxter equation naturally gives a coboundary noncommutative poisson bialgebra rota baxter operators more generally o operators on noncommutative poisson algebras and noncommutative pre poisson algebras are introduced by which we construct skew symmetric solutions of the poisson yang baxter equation in some special noncommutative poisson algebras obtained from these structures

novikov poisson algebras abstract we classify novikov poisson algebras whose novikov algebras are simple with an idempotent element moreover a class of simple novikov algebras without idempotent elements is constructed through novikov poisson algebras certain new simple lie superalgebras induced by novikov poisson algebras are introduced

structure of a new class of non graded infinite dimensional simple lie algebras abstract a new class of infinite dimensional simple lie algebras over a field with characteristic 0 are constructed these are examples of non graded lie algebras the isomorphism classes of these lie algebras are determined the structure space of these algebras is given explicitly

on fermionic novikov algebras novikov algebras were introduced in connection with the poisson brackets of hydrodynamic type and hamiltonian operators in formal variational calculus they are a class of left symmetric algebras with commutative right multiplication operators which can be viewed as bosonic fermionic novikov algebras are a class of left symmetric algebras with anti commutative right multiplication operators they correspond to a certain hamiltonian superoperator in a supervariable in this paper we commence a study on fermionic novikov algebras from the algebraic point of view we will show that any fermionic novikov algebra in dimension 3 must be bosonic moreover we give the classification of real fermionic novikov algebras on four dimensional nilpotent lie algebras and some examples in higher dimensions as a corollary we obtain kinds of four dimensional real fermionic novikov algebras which are not bosonic all of these examples will serve as a guide for further development including the application in physics

research on the relationship between the multifractality and long memory of realized volatility in the sseci abstract we examine the multifractal properties of the realized volatility rv and realized bipower variation rbv series in the shanghai stock exchange composite index sseci by using the multifractal detrended fluctuation analysis mf dfa method we find that there exist distinct multifractal characteristics in the volatility series the contributions of two different types of source of multifractality namely fat tailed probability distributions and nonlinear temporal correlations are studied by using the unit root test we also find the strength of the multifractality of the volatility time series is insensitive to the sampling frequency but that the long memory of these series is sensitive

classification of balinsky novikov superalgebras with dimension 2 2 the notion of balinsky novikov bn superalgebra was introduced to construct super virasoro type lie superalgebras we classify the 2 2 dimensional complex bn superalgebras whose odd parts products are not zero in addition to the known results on the classification of 2 2 dimensional novikov superalgebras we give an explicit comparison among them and their associated lie superalgebras as an application we construct some lie superalgebras whose even parts are the w 2 2 lie algebra finally we reformulate the classification results in terms of the even parts being the known classification results of two dimensional novikov algebras

rota baxter operators on 4 dimensional complex simple associative algebras rota baxter operators or relations were introduced to solve certain analytic and combinatorial problems and then applied to many fields in mathematics and mathematical physics in this paper we commence to study the rota baxter operators of weight zero on a 4 dimensional complex simple associative algebra which is isomorphic to the algebra of all 2x2 matrices over the field of complex numbers such operators satisfy the operator form of the classical yang baxter equation on the general linear lie algebra gl 2 c we provide two different solving methods one by hand to show some tricks for solving a large nonlinear system and another one by computer algebra to show the possibility of solving higher dimensional cases

hopf algebras of rooted forests cocyles and free rota baxter algebras the hopf algebra and the rota baxter algebra are the two algebraic structures underlying the algebraic approach of connes and kreimer to renormalization of perturbative quantum field theory in particular the hopf algebra of rooted trees serves as the baby model of feynman graphs in their approach and can be characterized by certain universal properties involving a hochschild 1 cocycle decorated rooted trees have also been applied to study feynman graphs we will continue the study of universal properties of various spaces of decorated rooted trees with such a 1 cocycle leading to the concept of a cocycle hopf algebra we further apply the universal properties to equip a free rota baxter algebra with the structure of a cocycle hopf algebra

multifractal detrended fluctuation analysis of nonstationary time series abstract we develop a method for the multifractal characterization of nonstationary time series which is based on a generalization of the detrended fluctuation analysis dfa we relate our multifractal dfa method to the standard partition function based multifractal formalism and prove that both approaches are equivalent for stationary signals with compact support by analyzing several examples we show that the new method can reliably determine the multifractal scaling behavior of time series by comparing the multifractal dfa results for original series with those for shuffled series we can distinguish multifractality due to long range correlations from multifractality due to a broad probability density function we also compare our results with the wavelet transform modulus maxima method and show that the results are equivalent

coherent stochastic resonance in a sextic double well potential abstract we study the response of a stochastic system described by the one dimensional fokker planck equation with a sextic double well potential u 6 x c 4 x 4 c 6 x 6 to a weak sinusoidal periodic signal two types of boundary conditions have been investigated i absorbing boundary conditions and ii natural boundary conditions the unperturbed propagators are calculated by the eigenfunction expansion method we find that for case i the mean survival time shows the coherent stochastic resonance and for case ii the signal to noise ratio exhibits the stochastic resonance the results are compared with those of the bistable quartic double well potential u 4 x 1 2 x 2 1 4 x 4

on spinor vertex operator algebras and their modules abstract in this paper we first present a generator theorem and introduce an asymmetric tensor of two colored vertex operator superalgebras with the same grading and supermap then we give axioms which characterize a class of vertex operator superalgebras constructed from clifford algebras in particular we are able to give a shorter argument for the jacobi identity than the existing proofs by using elements analogous to coherent states and our generator theorem using the new tensor and the same techniques we classify twisted irreducible modules of these algebras in a constructive way

classification of simple novikov algebras and their irreducible modules of characteristic 0 abstract in this paper we first present a classification theorem of simple infinite dimensional novikov algebras over an algebraically closed field of characteristic 0 then we classify all the irreducible modules of certain infinite dimensional simple novikov algebras with an idempotent element whose left action is locally finite

a presentation for the virasoro and super virasoro algebras it is shown that the entire virasoro ramond and neveu schwarz algebras can each be constructed from a finite number of well chosen generators satisfying a small number of conditions the most economical sets consist of just two starting generators in all cases subject to eight conditions for the virasoro case five conditions for the ramond case and nine conditions for the neveu schwarz case

analysis of the efficiency and multifractality of gold markets based on multifractal detrended fluctuation analysis abstract in this paper we investigate the efficiency and multifractality of a gold market based on multifractal detrended fluctuation analysis our evidence shows that the gold return series are multifractal both for time scales smaller than a month and for time scales larger than a month for time scales smaller than a month the main contribution of multifractality is fat tail distribution for time scales larger than a month both long range correlations and fat tail distribution play important roles in the contribution of multifractality using the method of rolling windows we find that the gold market became more and more efficient over time especially after 2001 the abnormal points of scaling exponents can also be related to some occasional events by defining a new inefficiency measure related to the multifractality we find that the gold market is more efficient during the upward periods than during the downward periods

the realization of non transitive novikov algebras novikov algebras were introduced in connection with hydrodynamic type poisson brackets and hamiltonian operators in the formal variational calculus we have given a kind of realization of transitive novikov algebras through the novikov algebras given by s gelfand and their compatible infinitesimal deformations in bai and meng 2001 j phys a math gen 34 3363 72 as a further and continuous study we extend this realization theory to the non transitive novikov algebras in the paper in two and three dimensions we find that all non transitive novikov algebras also can be realized as the novikov algebras given by s gelfand and their compatible infinitesimal deformations moreover they have simpler formulae

quasi hom lie algebras central extensions and 2 cocycle like identities this paper introduces the notion of a quasi hom lie algebra or simply a qhl algebra which is a natural generalization of hom lie algebras introduced in a previous paper j t hartwig d larsson s d silvestrov deformations of lie algebras using sigma derivations math qa 0408064 quasi hom lie algebras include also as special cases color lie algebras and superalgebras and can be seen as deformations of these by maps twisting the jacobi identity and skew symmetry the natural realm for these quasi hom lie algebras is generalizations deformations of the witt algebra delta of derivations on the laurent polynomials c t t 1 we also develop a theory of central extensions for qhl algebras which can be used to deform and generalize the virasoro algebra by centrally extending the deformed witt type algebras constructed here in addition we give a number of other interesting examples of quasi hom lie algebras among them a deformation of the loop algebra less

deformations of lie algebras using σ derivations in this article we develop an approach to deformations of the witt and virasoro algebras based on sigma derivations we show that sigma twisted jacobi type identity holds for generators of such deformations for the sigma twisted generalization of lie algebras modeled by this construction we develop a theory of central extensions we show that our approach can be used to construct new deformations of lie algebras and their central extensions which in particular include naturally the q deformations of the witt and virasoro algebras associated to q difference operators providing also corresponding q deformed jacobi identities c 2005 elsevier inc all rights reserved

new identities in dendriform algebras abstract dendriform structures arise naturally in algebraic combinatorics where they allow for example the splitting of the shuffle product into two pieces and through rota baxter algebra structures the latter appear among others in differential systems and in the renormalization process of pqft we prove new combinatorial identities in dendriform algebras that appear to be strongly related to classical phenomena such as the combinatorics of lyndon words rewriting rules in lie algebras or the fine structure of the malvenuto reutenauer algebra one of these identities is an abstract noncommutative dendriform generalization of the bohnenblust spitzer identity and of an identity involving iterated chen integrals due to c s lam

coherent stochastic resonance in a system with in out intermittency abstract we study the effect of noise on the properties of in out intermittency we add noise to a single variable of the system the one parallel to the invariant subspace at some magnitude of noise a new kind of coherent stochastic resonance is observed in which the average time spent near the invariant subspace has a maximum as a function of the magnitude of the noise we present numerical simulations of this phenomenon and a simple theoretical model using a markov chain

a koszul duality for props the notion of prop models the operations with multiple inputs and multiple outputs acting on some algebraic structures like the bialgebras or the lie bialgebras in this paper we generalize the koszul duality theory of associative algebras and operads to props

on the associative analog of lie bialgebras abstract an infinitesimal bialgebra is at the same time an associative algebra and coalgebra in such a way that the comultiplication is a derivation this paper continues the basic study of these objects with emphasis on the connections with the theory of lie bialgebras it is shown that non degenerate antisymmetric solutions of the associative yang baxter equation are in one to one correspondence with non degenerate cyclic 2 cocycles the associative and classical yang baxter equations are compared it is studied when a solution to the first is also a solution to the second necessary and sufficient conditions for obtaining a lie bialgebra from an infinitesimal one are found in terms of a canonical map that behaves simultaneously as a commutator and a cocommutator the class of balanced infinitesimal bialgebras is introduced they have an associated lie bialgebra several well known lie bialgebras are shown to arise in this way the construction of drinfeld s double from earlier work by the author in press in contemp math amer math soc providence for arbitrary infinitesimal bialgebras is complemented with the construction of the balanced double for balanced ones this construction commutes with the passage from balanced infinitesimal bialgebras to lie bialgebras

derivations of skew polynomial rings abstract let f be a field of characteristic 0 and let i j f for 1 i j n define r f x 1 x 2 x n to be the skew polynomial ring with x i x j i j x j x i and let s f x 1 x 2 x n x 11 x 12 x 1n be the corresponding laurent polynomial ring in a recent paper kirkman procesi and small considered these two rings under the assumption that s is simple and showed for example that the lie ring of inner derivations of s is simple furthermore when n 2 they determined the automorphisms of s related its ring of inner derivations to a certain block algebra and proved that every derivation of r is the sum of an inner derivation and a derivation which sends each xi to a scalar multiple of itself in this paper we extended these results to a more general situation specifically we study twisted group algebras ft g where g is a commutative group and f is a field of any characteristic furthermore we consider certain subalgebras ft h where h is a subsemigroup of g which generates g as a group finally if e g g f is a skew symmetric bilinear form then we study the lie algebra fe g associated with e and we consider its relationship to the lie structure defined on various twisted group algebras ft g

quadratic conformal superalgebras abstract in this paper we shall classify quadratic conformal superalgebras by certain compatible pairs of a lie superalgebra and a novikov superalgebra four general constructions of such pairs are given moreover we shall classify such pairs related to simple novikov algebras

f manifold algebras and deformation quantization via pre lie algebras abstract the notion of an f manifold algebra is the underlying algebraic structure of an f manifold we introduce the notion of pre lie formal deformations of commutative associative algebras and show that f manifold algebras are the corresponding semi classical limits we study pre lie infinitesimal deformations and extension of pre lie n deformation to pre lie n 1 deformation of a commutative associative algebra through the cohomology groups of pre lie algebras we introduce the notions of pre f manifold algebras and dual pre f manifold algebras and show that a pre f manifold algebra gives rise to an f manifold algebra through the sub adjacent associative algebra and the sub adjacent lie algebra we use rota baxter operators more generally o operators and average operators on f manifold algebras to construct pre f manifold algebras and dual pre f manifold algebras

on commutative polarizations let l be a finite dimensional lie algebra over a field k of characteristic zero and let u l be its enveloping algebra with quotient division ring d l let p be a commutative lie subalgebra of l in o2 the necessary and sufficient condition on p was given in order for d p to be a maximal commutative subfield of d l in particular this condition is satisfied if p is a commutative polarization cp with respect to any regular f l and the converse holds if l is ad algebraic the purpose of this paper is to study lie algebras admitting these cp s and to demonstrate their widespread occurrence first we have the following characterisation if l is completely solvable p is a cp of l if and only if there exists a descending chain of lie subalgebras

compatible o operators on bimodules over associative algebras abstract we recall the definition of the o operators on bimodules over associative algebras also called generalized rota baxter operators and we introduce the notions of compatible o operators and of o n structures we show that an o n structure gives rise to a hierarchy of o operators and that a solution of the strong maurer cartan equation on the associative twilled algebra associated to an o operator gives rise to a pair of o n structures which are naturally in duality we introduce the notions of pn n and p structures on associative algebras and study their relations

designing realised kernels to measure the ex post variation of equity prices in the presence of noise this paper shows how to use realised kernels to carry out efficient feasible inference on the expost variation of underlying equity prices in the presence of simple models of market frictions the issue is subtle with only estimators which have symmetric weights delivering consistent estimators with mixed gaussian limit theorems the weights can be chosen to achieve the best possible rate of convergence and to have an asymptotic variance which is close to that of the maximum likelihood estimator in the parametric version of this problem realised kernels can also be selected to i be analysed using endogenously spaced data such as that in databases on transactions ii allow for market frictions which are endogenous iii allow for temporally dependent noise the finite sample performance of our estimators is studied using simulation while empirical work illustrates their use in practice

classification of quasifinite modules over the lie algebras of weyl type abstract for a nondegenerate additive subgroup of the n dimensional vector space f n over an algebraically closed field f of characteristic zero there is an associative algebra and a lie algebra of weyl type w n spanned by all differential operators ud1m1 dnmn for u f the group algebra and m1 mn 0 where d1 dn are degree operators in this paper it is proved that an irreducible quasifinite w z 1 module is either a highest or lowest weight module or else a module of the intermediate series furthermore a classification of uniformly bounded w z 1 modules is completely given it is also proved that an irreducible quasifinite w n module is a module of the intermediate series and a complete classification of quasifinite w n modules is also given if is not isomorphic to z

bilinear forms on fermionic novikov algebras novikov algebras were introduced in connection with the poisson brackets of hydrodynamic type and hamiltonian operators in formal variational calculus fermionic novikov algebras correspond to a certain hamiltonian super operator in a super variable in this paper we show that there is a remarkable geometry on fermionic novikov algebras with non degenerate invariant symmetric bilinear forms which we call pseudo riemannian fermionic novikov algebras they are related to pseudo riemannian lie algebras furthermore we obtain a procedure to classify pseudo riemannian fermionic novikov algebras as an application we give the classification in dimension 4 motivated by the one in dimension 4 we construct some examples in high dimensions

hom gel fand dorfman bialgebras and hom lie conformal algebras the aim of this paper is to introduce the notions of hom gel fand dorfman bialgebra and hom lie conformal algebra in this paper we give four constructions of hom gel fand dorfman bialgebras also we provide a general construction of hom lie conformal algebras from hom lie algebras finally we prove that a hom gel fand dorfman bialgebra is equivalent to a hom lie conformal algebra of degree 2

bihom novikov algebras and infinitesimal bihom bialgebras abstract we introduce and study infinitesimal bihom bialgebras bihom novikov algebras bihom novikov poisson algebras and find some relations among these concepts our main result is to show how to obtain a left bihom pre lie algebra from an infinitesimal bihom bialgebra

forecasting the realized volatility of csi 300 abstract according to the characteristics of realized volatility existing in shanghai and shenzhen 300 index china securities index 300 csi 300 the garch family model is introduced to describe the arch effect of error sequences in har arfima and arfimax models then the har garch family the arfima garch family and the arfimax garch family models set is proposed which contains 33 kinds of models using the quasi maximum likelihood method the parameters of the all models are estimated with normal n and skewed student t skst distributions by rolling window technology one step ahead rolling prediction of realized volatility for csi 300 is conducted the results from prediction accuracy by model confidence set mcs test show that the realized volatility prediction models with skewed student t distribution possess higher precision than those of normal distribution in general the arfimax and other six models in arfimax garch family form the optimal prediction models set which can forecast the realized volatility of csi 300 with better accuracy

forecasting volatility of ssec in chinese stock market using multifractal analysis abstract in this paper taking about 7 years high frequency data of the shanghai stock exchange composite index ssec as an example we propose a daily volatility measure based on the multifractal spectrum of the high frequency price variability within a trading day an arfima model is used to depict the dynamics of this multifractal volatility mfv measures the one day ahead volatility forecasting performances of the mfv model and some other existing volatility models such as the realized volatility model stochastic volatility model and garch are evaluated by the superior prediction ability spa test the empirical results show that under several loss functions the mfv model obtains the best forecasting accuracy

pseudo riemannian novikov algebras novikov algebras were introduced in connection with the poisson brackets of hydrodynamic type and hamiltonian operators in formal variational calculus pseudo riemannian novikov algebras denote novikov algebras with nondegenerate invariant symmetric bilinear forms in this paper we find that there is a remarkable geometry on pseudo riemannian novikov algebras and give a special class of pseudo riemannian novikov algebras

on simple novikov algebras and their irreducible modules abstract we give a complete classification of finite dimensional simple novikov algebras and their irreducible modules over an algebraically closed field with prime characteristic moreover we introduce novikov poisson algebras and their tensor theory our tensor theory enables us to understand better certain finite dimensional simple novikov algebras and their irreducible modules

which is the better forecasting model a comparison between har rv and multifractality volatility abstract in this paper by taking the 5 min high frequency data of the shanghai composite index as example we compare the forecasting performance of har rv and multifractal volatility realized volatility realized bipower variation and their corresponding short memory model with rolling windows forecasting method and the model confidence set which is proved superior to spa test the empirical results show that for six loss functions har rv outperforms other models moreover to make the conclusions more precise and robust we use the mcs test to compare the performance of their logarithms form models and find that the har log rv has a better performance in predicting future volatility furthermore by comparing the two models of har rv and har log rv we conclude that in terms of performance forecasting the har log rv model is the best model among models we have discussed in this paper

supersymmetric extension of the korteweg de vries equation it is shown that among a one parameter family of supersymmetric extensions of the korteweg de vries equation there is a special system that has an infinite number of conservation laws which can be formulated in the second hamiltonian structure and which has a nontrivial lax representation its modified version is also discussed

two state intermittency near a symmetric interaction of saddle node and hopf bifurcations a case study from dynamo theory we consider a model of a hopf bifurcation interacting as a codimension 2 bifurcation with a saddle node on a limit cycle motivated by a low order model for magnetic activity in a stellar dynamo this model consists of coupled interactions between a saddle node and two hopf bifurcations where the saddle node bifurcation is assumed to have global reinjection of trajectories the model can produce chaotic behaviour within each of a pair of invariant subspaces and also it can show attractors that are stuck on to both of the invariant subspaces we investigate the detailed intermittent dynamics for such an attractor investigating the effect of breaking the symmetry between the two hopf bifurcations and observing that it can appear via blowout bifurcations from the invariant subspaces we give a simple markov chain model for the two state intermittent dynamics that reproduces the time spent close to the invariant subspaces and the switching between the different possible invariant subspaces this clarifies the observation that the proportion of time spent near the different subspaces depends on the average residence time and also on the probabilities of switching between the possible subspaces

novikov algebras with associative bilinear forms novikov algebras were introduced in connection with the poisson brackets of hydrodynamic type and hamiltonian operators in formal variational calculus the goal of this paper is to study novikov algebras with non degenerate associative symmetric bilinear forms which we call quadratic novikov algebras based on the classification of solvable quadratic lie algebras of dimension not greater than 4 and novikov algebras in dimension 3 we show that quadratic novikov algebras up to dimension 4 are commutative furthermore we obtain the classification of transitive quadratic novikov algebras in dimension 4 but we find that not every quadratic novikov algebra is commutative and give a non commutative quadratic novikov algebra in dimension 6

forecasting stock market volatility do realized skewness and kurtosis help abstract in this study we investigate the predictability of the realized skewness rsk and realized kurtosis rku to stock market volatility that has not been addressed in the existing studies out of sample results show that rsk which can significantly improve forecast accuracy in mid and long term is more powerful than rku in forecasting volatility whereas these variables are useless in short term forecasting furthermore we employ the realized kernel rk for the robustness analysis and the conclusions are consistent with the rv measures our results are of great importance for portfolio allocation and financial risk management

from rota baxter algebras to pre lie algebras rota baxter algebras were introduced to solve some analytic and combinatorial problems and have appeared in many fields in mathematics and mathematical physics rota baxter algebras provide a construction of pre lie algebras from associative algebras in this paper we give all rota baxter operators of weight 1 on complex associative algebras in dimension 3 and their corresponding pre lie algebras

forecasting the value at risk of chinese stock market using the harq model and extreme value theory abstract using intraday data of the csi300 index this paper discusses value at risk var forecasting of the chinese stock market from the perspective of high frequency volatility models first we measure the realized volatility rv with 5 minute high frequency returns of the csi300 index and then model it with the newly introduced heterogeneous autoregressive quarticity harq model which can handle the time varying coefficients of the har model second we forecast the out of sample var of the csi300 index by combining the harq model and extreme value theory evt finally using several popular backtesting methods we compare the var forecasting accuracy of harq model with other traditional har type models such as har har j char and shar the empirical results show that the novel harq model can beat other har type models in forecasting the var of the chinese stock market at various risk levels

hom novikov algebras we study a twisted generalization of novikov algebras called hom novikov algebras in which the two defining identities are twisted by a linear map it is shown that hom novikov algebras can be obtained from novikov algebras by twisting along any algebra endomorphism all algebra endomorphisms on complex novikov algebras of dimensions 2 or 3 are computed and their associated hom novikov algebras are described explicitly another class of hom novikov algebras is constructed from hom commutative algebras together with a derivation generalizing a construction due to dorfman and gel fand two other classes of hom novikov algebras are constructed from hom lie algebras together with a suitable linear endomorphism generalizing a construction due to bai and meng

deformations of associative rota baxter operators abstract rota baxter operators and more generally o operators on associative algebras are important in probability combinatorics associative yang baxter equation and splitting of algebras using a method of uchino we construct an explicit graded lie algebra whose maurer cartan elements are given by o operators this allows us to construct cohomology for an o operator this cohomology can also be seen as the hochschild cohomology of a certain algebra with coefficients in a suitable bimodule next we study linear and formal deformations of an o operator which are governed by the above defined cohomology we introduce nijenhuis elements associated with an o operator which give rise to trivial deformations as applications we conclude deformations of weight zero rota baxter operators associative r matrices and averaging operators

variational calculus of supervariables and related algebraic structures abstract we establish a formal variational calculus of supervariables which is a combination of the bosonic theory of gel fand dikii and the fermionic theory in our earlier work certain interesting new algebraic structures are found in connection with hamiltonian superoperators in terms of our theory in particular we find connections between hamiltonian superoperators and novikov poisson algebras that we introduced in our earlier work in order to establish a tensor theory of novikov algebras furthermore we prove that an odd linear hamiltonian superoperator in our variational calculus induces a lie superalgebra which is a natural generalization of the super virasoro algebra under certain conditions

gelfand dorfman algebras derived identities and the manin product of operads abstract gelfand dorfman bialgebras gd algebras are nonassociative systems with two bilinear operations satisfying a series of identities that express hamiltonian property of an operator in the formal calculus of variations the paper is devoted to the study of gd algebras related with differential poisson algebras as a byproduct we obtain a general description of identities that hold for operations a b d a b and a b a d b on a non associative differential algebra with a derivation d

on free gelfand dorfman novikov poisson algebras and a pbw theorem abstract in 1997 x xu 18 19 invented a concept of novikov poisson algebras we call them gelfand dorfman novikov poisson gdn poisson algebras we construct a linear basis of a free gdn poisson algebra we define a notion of a special gdn poisson admissible algebra based on x xu s definition and an s i gelfand s observation see 9 it is a differential algebra with two commutative associative products and some extra identities we prove that any gdn poisson algebra is embeddable into its universal enveloping special gdn poisson admissible algebra also we prove that any gdn poisson algebra with the identity x y z x y z x z y is isomorphic to a commutative associative differential algebra

pairs of compatible associative algebras classical yang baxter equation and quiver representations given an associative multiplication in matrix algebra compatible with the usual one or in other words a linear deformation of the matrix algebra we construct a solution to the classical yang baxter equation we also develop a theory of such deformations and construct numerous examples it turns out that these deformations are in one to one correspondence with representations of certain algebraic structures which we call m structures we also describe an important class of m structures related to the affine dynkin diagrams of a d e type these m structures and their representations are described in terms of quiver representations

on the realization of transitive novikov algebras novikov algebras were introduced in connection with the poisson brackets of hydrodynamic type and hamiltonian operators in the formal variational calculus it is well known that the radical of a finite dimensional novikov algebra is transitive in this paper we prove that a kind realization of novikov algebras given by s gel fand is transitive and we give a deformation theory of novikov algebras in two and three dimensions we find that all transitive novikov algebras can be realized as the novikov algebras given by s gel fand and their compatible infinitesimal deformations

the automorphisms of novikov algebras in low dimensions novikov algebras were introduced in connection with poisson brackets of hydrodynamic type and hamiltonian operators in the formal variational calculus they also correspond to a class of vertex algebras an automorphism of a novikov algebra is a linear isomorphism satisfying xy x y which keeps the algebraic structure the set of automorphisms of a novikov algebra is a lie group whose lie algebra is just the novikov algebra s derivation algebra the theory of automorphisms plays an important role in the study of novikov algebras in this paper we study the automorphisms of novikov algebras we get some results on their properties and classification in low dimensions these results are fundamental in a certain sense and they will serve as a guide for further development moreover we apply these results to classify gel fand dorfman bialgebras and novikov poisson algebras these results also can be used to study certain phase spaces and geometric classical r matrices