parameter transformations for improved approximate confidence regions in nonlinear least squares in a previous paper it was shown that parameter effects nonlinearities of a nonlinear regression model experimental design parameterization combination can be quantified by means of a parameter effects curvature array a based on second derivatives of the model function in this paper the individual terms of a are interpreted and local compensation methods are suggested a method of computing the parameter effects array corresponding to a transformed set of parameters is given and we discuss how this result could be used to determine reparameterizations which have zero local parameter effects nonlinearity

the five dimensional complete left symmetric algebra structures compatible with an abelian lie algebra structure abstract the classification of five dimensional complete left symmetric algebras is known to be a hard problem in this paper we establish an explicit classification of the five dimensional complete left symmetric algebras over r having an abelian associated lie algebra a detailed list of all possible isomorphism types is presented

curvature adjusted optimal design of sampling times for the inference of pharmacokinetic compartment models in pharmacokinetics compartment models are often used to describe the time course of blood concentration after the administration of a drug in this article we propose an optimal design criterion for precise estimation of parameters included in the compartment model and illustrate the non sequential design of sampling times of blood drug concentration data in individual pharmacokinetics the proposed optimal design criterion minimizes the determinant of the mean squared error matrix of the parameter estimator that is quadratically approximated by the curvature array therefore the proposed criterion considers the intrinsic and parameter effects nonlinearity underlying the compartment model and so is applicable in a pharmacokinetic experiment where the sample size of the blood drug concentration data is quite small

translations in simply transitive affine actions of heisenberg type lie groups let g be a 2 step nilpotent lie group with a 1 dimensional commutator subgroup we prove that for any simply transitive and affine action of g there exists a non trivial subgroup of g acting as pure translations this result no longer holds in case the commutator subgroup is higher dimensional

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

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

multiple emitter location and signal parameter estimation processing the signals received on an array of sensors for the location of the emitter is of great enough interest to have been treated under many special case assumptions the general problem considers sensors with arbitrary locations and arbitrary directional characteristics gain phase polarization in a noise interference environment of arbitrary covariance matrix this report is concerned first with the multiple emitter aspect of this problem and second with the generality of solution a description is given of the multiple signal classification music algorithm which provides asymptotically unbiased estimates of 1 number of incident wavefronts present 2 directions of arrival doa or emitter locations 3 strengths and cross correlations among the incident waveforms 4 noise interference strength examples and comparisons with methods based on maximum likelihood ml and maximum entropy me as well as conventional beamforming are included an example of its use as a multiple frequency estimator operating on time series is included

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

left symmetric algebras from linear functions abstract in this paper some left symmetric algebras are constructed from linear functions they include a kind of simple left symmetric algebras and some examples appearing in mathematical physics their complete classification is also given which shows that they can be regarded as generalization of certain two dimensional left symmetric algebras

performance analysis of music type high resolution estimators for direction finding in correlated and coherent scenes an asymptotic analysis is presented of a class of high resolution estimators for resolving correlated and coherent plane waves in noise these estimators are in turn constructed from certain eigenvectors associated with spatially smoothed or unsmoothed covariance matrices generated from a uniform array the analysis is first carried out for the smoothed case and from this the conventional i e unsmoothed multiple signal classification music scheme follows as a special case independent of the total number of sources present in the scene the variance of the conventional music estimator along the true arrival angles is shown to be zero within a first order approximation the bias expressions in the smoothed case are used to obtain a resolution threshold for two coherent equipowered plane waves in white noise and the result is compared to the one derived by kaveh et al 1986 for two uncorrelated equipowered plane waves

left symmetric algebra structures on the w algebra w 2 2 we study the compatible left symmetric algebra structures on the w algebra w 2 2 with some natural grading conditions the results of earlier work on left symmetric algebra structures on the virasoro algebra play an essential role in determining these compatible structures as a corollary any such left symmetric algebra contains an infinite dimensional trivial subalgebra that is also a submodule of the regular module

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

a resolution measure for the music algorithm and its application to plane wave arrivals contaminated by coherent interference the authors present a deterministic approach to the resolution analysis of the music algorithm for resolving plane waved contaminated by coherent interference when ensemble average covariance matrices are used a resolution measure to describe the resolution potential of music in resolving two plane waves in noise is introduced a closed form solution for the resolution measure is given and the result is compared to the resolution threshold derived by m kaveh and a j barabell 1986 when the covariance matrices are estimated from a finite number of snapshots an approximate expression for the threshold signal to interference ratio sir is derived for the cases when sirs are large and the coherent interference and direct arrivals are well separated in spatial frequency illustrations are given using an 11 element uniform array for the cases of plane wave reflection from an infinite plane and scattering from an infinite conducting circular cylinder

marginal curvatures and their usefulness in the analysis of nonlinear regression models abstract interval estimation for individual parameters in nonlinear regression is examined in relation to curvature of the solution locus criteria are developed to define severe curvature and distinguish cases in which linear methods may be used from those in which parameter transformations are necessary a formula for improving the linear approximation in cases of relatively mild curvature is proposed for example suppose that interest is focused on one specific parameter j from among 1 2 p in a nonlinear regression model a crude approach to setting 95 confidence limits to j might proceed as follows first calculate the standard error of the estimate as the square root of its asymptotic variance then call the confidence limits in this article higher order correction terms and are proposed that enable us to develop a power series expansion for the confidence limits as and respectively here denotes some estimate of 2 the variance of a single observation

affine manifolds and orbits of algebraic groups this paper is the sequel to the radiance obstruction and parallel forms on a ffne manifolds lyans amer math soc 286 1984 629 649 which introduced a new family of secondary characteristic classes for affine structures on manifolds the present paper utilizes the representation of these classes in lie algebra cohomology and algebraic group cohomology to deduce new results relating the geometric properties of a compact affine manifold mn to the action on rn of the algebraic hull a r of the affine holonomy group r c aff rn a main technical result of the paper is that if m has a nonzero cohomology class represented by a parallel k form then every orbit of a r has dimension k when m is compact then a r acts transitively provided that m is complete or has parallel volume the converse holds when r is nilpotent a 4 dimensional subgroup of aff r3 is exhibited which does not contain the holonomy group of any compact affine 3 manifold when m has solvable holonomy and is complete then m must have parallel volume conversely if m has parallel volume and is of the homotopy type of a solvmanifold then m is complete if m is a compact homogeneous affine manifold or if m possesses a rational riemannian metric then it is shown that the conditions of parallel volume and completeness are equivalent this paper is the sequel to our previous paper 22 in that paper we exploited certain characteristic classes exterior powers of the radiance obstruction to obtain relationships between various properties of affine manifolds our results supported the conjecture first made by l markus 36 that a compact affine manifold is complete if and only if it has parallel volume we shall refer to this as the main conjecture let m be a compact affine manifold with developing map dev m e and affine holonomy representation h 7r h 7r r c aff e here 1r is the group of deck transformations of the universal cover m e is the vector space rn and aff e is the group of affine automorphisms of e the map dev is a locally affine immersion which is equivariant respecting h the linear holonomy homb morphism is the composition a 1r gl e of h with the natural homomorphism l aff e gl e the obstruction to r fixing a point in e is a 1 dimensional cohomology class cm e h1 m ex with coefficients in e twisted by a it comes from a universal class in the group cohomology h1 aff e el which contains the crossed homomorphism u aff e e g g 0 received by the editors december 12 1984 and in revised form may 29 1985 1980 mathematics subject classification 1985 revision primary 57r99 53c05 secondary 53c10 55r25 1 research partially supported by fellowships and grants from the national science foundation a 1986 american mathematical society 0002 9947 86 1 00 25 per page

commutative post lie algebra structures and linear equations for nilpotent lie algebras abstract we show that for a given nilpotent lie algebra g with z g g g all commutative post lie algebra structures or cpa structures on g are complete this means that all left and all right multiplication operators in the algebra are nilpotent then we study cpa structures on free nilpotent lie algebras f g c and discover a strong relationship to solving systems of linear equations of type x u y v 0 for generator pairs x y f g c we use results of remeslennikov and stohr concerning these equations to prove that for certain g and c the free nilpotent lie algebra f g c has only central cpa structures

the statistical performance of the music and the minimum norm algorithms in resolving plane waves in noise this paper presents an asymptotic statistical analysis of the null spectra of two eigen assisted methods music 1 and minimum norm 2 for resolving independent closely spaced plane waves in noise particular attention is paid to the average deviation of the null spectra from zero at the true angles of arrival for the plane waves these deviations are expressed as functions of signal to noise ratios number of array elements angular separation of emitters and the number of snapshots in the case of music an approximate expression is derived for the resolution threshold of two plane waves with equal power in noise this result is validated by monte carlo simulations

a unified algebraic approach to the classical yang baxter equation in this paper the different operator forms of the classical yang baxter equation are given in the tensor expression through a unified algebraic method it is closely related to left symmetric algebras which play an important role in many fields in mathematics and mathematical physics by studying the relations between left symmetric algebras and the classical yang baxter equation we can construct left symmetric algebras from certain classical r matrices and conversely there is a natural classical r matrix constructed from a left symmetric algebra which corresponds to a parakahler structure in geometry moreover the former in a special case gives an algebraic interpretation of the left symmetry as a lie bracket left twisted by a classical r matrix

robust estimation of sinusoidal signals with colored noise using decentralized processing a technique is developed for the estimation of the number of signals and their central frequencies using decentralized processing when it is known a priori that the observations consist of a finite number of sinusoidal signals corrupted by an additive colored random noise process with unknown correlations such a noise sequence may be caused by jamming from a hostile agent the authors decentralized processing scheme is one in which each sensor estimates the frequencies and their covariance matrix and sends the results to the fusion center at the fusion center since the estimates from the sensors have a mixture density that is possibly not gaussian a robust technique is utilized to combine the estimates even when the numbers of frequencies transmitted by the various sensors are identical determining corresponding frequencies from each sensor is not a straightforward task also outliers caused by line splitting or by spurious frequencies are hard to detect these problems can be resolved by two methods the so called refitting method and the ranking method algorithms for both are presented in detail

abelian hessian algebra and commutative frobenius algebra in this paper we study the structure of an abelian hessian algebra first we show that it can be decomposed into unital abelian hessian algebras and a complete abelian hessian algebra abbreviated by caha then we show that a unital one is in fact a hyperbolic extension of a caha next we investigate the structure of caha by studying double filtration obtained canonically from lower and upper annihilator series this double filtration together with j invariant of ternary cubic form give a complete classification of caha up to dimension 6

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

the structure of assosymmetric algebras in this paper we study the structure of an assosymmetric algebra a by investigating various radicals and show that the wedderburn principal theorem holds when a r a has no 1 dimensional factor where r a is the radical of a and also discuss a pierce decomposition of a

left symmetric structures on simple modular lie algebras abstract this paper investigates left symmetric structures on finite dimensional simple lie algebras g over a field k if k is of characteristic 0 then g does not admit any left symmetric structure this is known in the theory of affine manifolds in the modular case however such structures may exist the main purpose of this paper is to show that classical simple lie algebras of characteristic p 3 admit left symmetric structures only in case p divides dim g the proof involves the computation of the first cohomology groups of classical lie algebras for certain g modules of small dimension here g is regarded as the lie algebra of a connected semisimple algebraic group over an algebraically closed field of characteristic p 0 most of these computations are due to jantzen for nonrestricted simple lie algebras of cartan type it is shown that many more left symmetric structures can be found one studies so called adjoint structures induced by nonsingular derivations of g the simple algebra l g of block of dimension pn 1 for example admits adjoint structures for every p 0 if p 2 the results are more complicated

improved methodology for parameter inference in nonlinear hydrologic regression models a new method is developed for the construction of reliable marginal confidence intervals and joint confidence regions for the parameters of nonlinear hydrologic regression models a parameter power transformation is combined with measures of the asymptotic bias and asymptotic skewness of maximum likelihood estimators to determine the transformation constants which cause the bias or skewness to vanish these optimized constants are used to construct confidence intervals and regions for the transformed model parameters using linear regression theory the resulting confidence intervals and regions can be easily mapped into the original parameter space to give close approximations to likelihood method confidence intervals and regions for the model parameters unlike many other approaches to parameter transformation the procedure does not use a grid search to find the optimal transformation constants an example involving the fitting of the michaelis menten model to velocity discharge data from an australian gauging station is used to illustrate the usefulness of the methodology

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

the classification of novikov algebras in low dimensions invariant bilinear forms in this note we give a complete classification of the non degenerate symmetric invariant bilinear forms on novikov algebras in dimension 2 and 3 which can be regarded as an addendum of the classification of novikov algebras in low dimensions given in our previous work bai c m and meng d j 2001 j phys a math gen 34 1581 94

the resolution threshold of music with unkown spatially colored noise in this correspondence we present a resolution analysis for the music algorithm in a spatially colored noise environment by applying wilkinson s first order perturbation theory to the colored noise term we have shown that the music spectrum estimates at spa tial frequencies of plane wave arrivals are proportional to the square of array signal to interference ratio asir and that the resolution threshold asir for a uniform array is proportional to the inverse square of normalized spatial frequency separation between two ar rivals derivations and simulations are given for the case of two equi power plane wave arrivals the presence of unknown spatially colored noise in spatial fre quency estimation of plane wave arrivals can cause significant per formance degradation for the music algorithm for signal arrivals in a spatially white noise environment a complete eigenspace sep aration between signal subspace and noise subspace can be ob tained and music spectrum exhibits infinite peaks at signal fre quencies in a spatially colored noise scn environment an eigenspace separation with such properties can be made only if the correlation structure of the scn is known a priori i for an un known scn any partitioned subspace designated as the signal sub space will include components from part of the scn and the or thogonal relation between signal direction vectors and the noisc subspace will be destroyed as a result spectral peaks in the mu sic estimator are finite and resolutions are limited in this paper spatially colored noise scn is radiation sources whose spatial correlation matrix has a nonidentity structure spa tially colored noise typically arises from sources continuously dis tributed in spatial frequency examples are cosmic noise and at mospheric noise it also arises from additive sensor noise sources when they are nonwhite with unknown correlations or when they are uncorrelated but of unequal powers mathematically scn may be represented by a matrix component q in a spatial correlation matrix r 1

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

commutative post lie algebra structures on lie algebras abstract we show that any cpa structure commutative post lie algebra structure on a perfect lie algebra is trivial furthermore we give a general decomposition of inner cpa structures and classify all cpa structures on complete lie algebras as a special case we obtain the cpa structures of parabolic subalgebras of semisimple lie algebras

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

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

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

statistical evaluation and choice of soil water retention models 1 this paper presents the results of statistical investigations for the evaluation of soil water retention models swrms we employed three different methods developed for model selection in the field of nonlinear regression namely simulation studies analysis of nonlinearity measures and resampling strategies such as cross validation and bootstrap methods using these methods together with small data sets we evaluated the performance of three exemplarily chosen types of swrms with respect to their parameter properties and the reliability of model predictions the resulting rankings of models show that the favorable models are characterized by few parameters with an almost linear estimation behavior and close to symmetric distributions to further demonstrate the potential of the statistical methods in the field of model selection a modification of the four parameter van genuchten model is proposed which shows significantly improved and robust statistical properties

bias in nonlinear regression abstract this document investigates the biases of the residuals and the maximum likelihood parameters estimates from standard normal theory nonlinear regression models emphasis is placed on determining the influence of individual cases on the biases and on understanding how the residual biases can affect the usefulness of standard diagnostic methods it is shown that the various bias expressions in the literature are equivalent that the biases in nonlinear regression can be studied usefully in the context of linear regression and that diagnostic plots using residuals can be misleading because of substantial residual biases for a class of partially nonlinear models it is shown that the maximum intrinsic curvature is closely related to the residual expectations finally the model associated with power transformations of single explanatory variables in linear regression is investigated in further detail and several numerical illustrations are presented author

commutative post lie algebra structures on nilpotent lie algebras and poisson algebras abstract we give an explicit description of commutative post lie algebra structures on some classes of nilpotent lie algebras for non metabelian filiform nilpotent lie algebras and lie algebras of strictly upper triangular matrices we show that all cpa structures are associative and induce an associated poisson admissible algebra

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

music maximum likelihood and cramer rao bound the performance of the music and ml methods is studied and their statistical efficiency is analyzed the cramer rao bound crb for the estimation problems is derived and some useful properties of the crb covariance matrix are established the relationship between the music and ml estimators is investigated as well a numerical study is reported of the statistical efficiency of the music estimator for the problem of finding the directions of two plane waves using a uniform linear array an exact description of the results is included

left symmetric algebras for mathfrak gl n we study the classification problem for left symmetric algebras with commutation lie algebra gr n in characteristic 0 the problem is equivalent to the classification of etale affine representations of g n algebraic invariant theory is used to characterize those modules for the algebraic group sl n which belong to affine etale representations of gr n from the classification of these modules we obtain the solution of the classification problem for gl n as another application of our approach we exhibit left symmetric algebra structures on certain reductive lie algebras with a one dimensional center and a non simple semisimple ideal

a zassenhaus conjecture and cpa structures on simple modular lie algebras abstract commutative post lie algebra structures on lie algebras in short cpa structures have been studied over fields of characteristic zero in particular for real and complex numbers motivated by geometry a perfect lie algebra in characteristic zero only admits the trivial cpa structure in this article we study these structures over fields of characteristic p 0 we show that every perfect modular lie algebra in characteristic p 2 having a solvable outer derivation algebra admits only the trivial cpa structure this involves a conjecture by hans zassenhaus saying that the outer derivation algebra out g of a simple modular lie algebra g is solvable we try to summarize the known results on the zassenhaus conjecture and prove some new results using the classification of simple modular lie algebras by premet and strade for algebraically closed fields of characteristic p 3 as a corollary we obtain that every central simple modular lie algebra of characteristic p 3 admits only the trivial cpa structure

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

polynomial alternatives for the group of affine motions it is known that every polycyclic by finite group even if it admits no affine structure allows a polynomial structure of bounded degree a major obstacle to a further development of the theory of these polynomial structures is that the group of the polynomial diffeomorphisms of mathbb r n in contrast to the group of affine motions is no longer a finite dimensional lie group in this paper we construct a family of finite dimensional lie groups even linear algebraic groups of polynomial diffeomorphisms which we call weighted groups of polynomial diffeomorphisms it turns out that every polycyclic by finite group admits a polynomial structure via these weighted groups in the nilpotent and other case s we can sharpen by specifying a nice set of weights the existence results obtained in earlier work we introduce unipotent polynomial structures of nilpotent groups and show how the existence of such polynomial structures is closely related to the existence of simply transitive actions of the corresponding mal cev completion this and other properties provide a strong analogy with the situation of affine structures and simply transitive affine actions considered e g in the work of fried goldman and hirsch

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