exponential codimension growth of pi algebras an exact estimate abstract letabe an associative pi algebra over a fieldfof characteristic zero by studying the exponential behavior of the sequence of codimensions cn a ofa we prove thatinv a limn c n a always exists and is an integer we also give an explicit way for computing such integer letbbe a finite dimensionalz2 graded algebra whose grassmann envelopeg b satisfies the same identities ofa theninv a inv g b dim c 0 dim c 1 wherec 0 c 1 is a suitablez2 graded semisimple subalgebra ofb

representability and specht problem for g graded algebras abstract let w be an associative pi algebra over a field f of characteristic zero graded by a finite group g let id g w denote the t ideal of g graded identities of w we prove 1 g graded pi equivalence there exists a field extension k of f and a finite dimensional z 2 z g graded algebra a over k such that id g w id g a where a is the grassmann envelope of a 2 g graded specht problem the t ideal id g w is finitely generated as a t ideal 3 g graded pi equivalence for affine algebras let w be a g graded affine algebra over f then there exists a field extension k of f and a finite dimensional algebra a over k such that id g w id g a

identities and central polynomials with involution for the grassmann algebra abstract let e be the infinite dimensional grassmann algebra over an infinite field of characteristic p different from 2 given an involution on e denote by i d e and c e the set of all polynomial identities and central polynomials of e respectively in this paper we describe i d e and c e moreover we prove that c e is not finitely generated as a t space if p 2

closed form approximations for optimal r q and s t policies in a parallel processing environment we consider a single item continuous review r q inventory system with a renewal demand process and independent identically distributed stochastic lead times using a stationary marked point process technique and a heavy traffic limit we prove a previous conjecture that inventory position and inventory on order are asymptotically independent we also establish closed form expressions for the optimal policy parameters and system cost in heavy traffic limit the first of their kind to our knowledge these expressions sharpen our understanding of the key determinants of the optimal policy and their quantitative and qualitative impacts for example the results demonstrate that the well known square root relationship between the optimal order quantity and demand rate under a sequential processing environment is replaced by the cube root under a stochastic parallel processing environment we further extend the study to periodic review s t systems with constant lead times the electronic companion is av

graded identities of matrix algebras and the universal graded algebra in the last decade group gradings and graded identities of finite dimensional central simple algebras have been an active area of research we refer the reader to bahturin et al 6 and 7 there are two basic kinds of group grading elementary and fine it was proved by bahturin and zaicev 7 that any group grading of mn c is given by a certain composition of an elementary grading and a fine grading in this paper we are concerned with fine gradings on mn c and their corresponding graded identities let r be a simple algebra finite dimensional over its center k and g a finite group we say that r is fine graded by g if r g grg is a grading and dimk rg 1 thus any component is either 0 or isomorphic to k as a k vector space it is easy to show that supp r the subset of elements of g for which rg is not 0 is a subgroup of g moreover

sharp derivative bounds for solutions of degenerate semi linear partial differential equations abstract the paper is a continuation of the kusuoka stroock programme of establishing smoothness properties of solutions of possibly degenerate partial differential equations by using probabilistic methods we analyze here a class of semi linear parabolic partial differential equations for which the linear part is a second order differential operator of the form v 0 i 1 n v i 2 where v 0 v n are first order differential operators that satisfy the so called ufg condition see kusuoka and stroock 1987 16 which is weaker than the hormander one specifically we prove that the bounds of the higher order derivatives of the solution along the vector fields coincide with those obtained in the linear case when the boundary condition is lipschitz continuous but that the asymptotic behavior of the derivatives may change because of the simultaneity of the nonlinearity and of the degeneracy when the boundary condition is of polynomial growth and measurable only

star polynomial identities computing the exponential growth of the codimensions abstract can one compute the exponential rate of growth of the codimensions of a pi algebra with involution over a field of characteristic zero it was shown in 2 that any such algebra a has the same identities as the grassmann envelope of a finite dimensional superalgebra with superinvolution b here by exploiting this result we are able to provide an exact estimate of the exponential rate of growth e x p a of any pi algebra a with involution it turns out that e x p a is an integer and in case the base field is algebraically closed it coincides with the dimension of an admissible subalgebra of maximal dimension of b

on the codimension sequence of g simple algebras abstract let f be an algebraically closed field of characteristic zero and let g be a finite group in this paper we will show that the asymptotics of c n g a the g graded codimension sequence of a finite dimensional g simple f algebra a has the form n 1 dim f a e 2 dim f a n as conjectured by e aljadeff d haile and m natapov where is some positive real number and a e denotes the identity component of a in the special case where a is the algebra of m m matrices with an arbitrary elementary g grading we succeeded in calculating the constant explicitly

graded polynomial identities as identities of universal algebras abstract let a and b be finite dimensional simple algebras with arbitrary signature over an algebraically closed field suppose a and b are graded by a semigroup s so that the graded identical relations of a are the same as those of b then a is isomorphic to b as an s graded algebra

the exponent for superalgebras with superinvolution abstract let a be a superalgebra with superinvolution over a field of characteristic zero and let c n a n 1 2 be its sequence of codimensions in 6 it was proved that such a sequence is exponentially bounded in this paper we capture this exponential growth for finitely generated superalgebras with superinvolution a over an algebraically closed field of characteristic zero we shall prove that lim n c n a n exists and it is an integer denoted exp a and called exponent of a moreover we shall characterize finitely generated superalgebras with superinvolution according to their exponent

quantum group gauge theory on quantum spaces we construct quantum group valued canonical connections on quantum homogeneous spaces including aq deformed dirac monopole on the quantum sphere of podles with quantum differential structure coming from the 3d calculus of woronowicz onsu q 2 the construction is presented within the setting of a general theory of quantum principal bundles with quantum group hopf algebra fibre associated quantum vector bundles and connection one forms both the base space spacetime and the total space are non commutative algebras quantum spaces

on twisting of finite dimensional hopf algebras in this paper we study the properties of drinfeld s twisting for finite dimensional hopf algebras we determine how the integral of the dual to a unimodular hopf algebra h changes under twisting of h we show that the classes of cosemisimple unimodular cosemisimple involutive cosemisimple quasitriangular finite dimensional hopf algebras are stable under twisting we also prove the cosemisimplicity of a coalgebra obtained by twisting of a cosemisimple unimodular hopf algebra by two different twists on two sides such twists are closely related to bi galois extensions and describe the representation theory of its dual next we define the notion of a non degenerate twist for a hopf algebra h and set up a bijection between such twists for h and h this bijection is based on miyashita ulbrich actions of hopf algebras on simple algebras it generalizes to the non commutative case the procedure of inverting a non degenerate skew symmetric bilinear form on a vector space finally we apply these results to classification of twists in group algebras and of cosemisimple triangular finite dimensional hopf algebras in positive characteristic generalizing the previously known classification in characteristic zero

p i algebras with hopf algebra actions abstract ifais a p i algebra in characteristic zero with action from a finite dimensional semisimple hopf algebrah thenahas a nilpotenth idealnsuch thata nwill beh verbally semiprime everyh verbally semiprime algebra ish p i equivalent to a direct sum ofh verbally prime algebras in the case of a finite group action or a grading by an abelian group we show that the sum can be taken to be finite in the case of an action by a finite cyclic groupg we classify allg p i algebras up to equivalence this paper generalizes the work of a r kerner 1985 math ussr izv 25

strong connections on quantum principal bundles a gauge invariant notion of a strong connection is presented and characterized it is then used to justify the way in which a global curvature form is defined strong connections are interpreted as those that are induced from the base space of a quantum bundle examples of both strong and non strong connections are provided in particular such connections are constructed on a quantum deformation of the two sphere fibrations2 rp2 a certain class of stronguq 2 connections on a trivial quantum principal bundle is shown to be equivalent to the class of connections on a free module that are compatible with theq dependent hermitian metric a particular form of the yang mills action on a trivialuq 2 bundle is investigated it is proved to coincide with the yang mills action constructed by a connes and m rieffel furthermore it is shown that the moduli space of critical points of this action functional is independent ofq

graded polynomial identities and codimensions computing the exponential growth abstract let g be a finite abelian group and a a g graded algebra over a field of characteristic zero this paper is devoted to a quantitative study of the graded polynomial identities satisfied by a we study the asymptotic behavior of c n g a n 1 2 the sequence of graded codimensions of a and we prove that if a satisfies an ordinary polynomial identity lim n c n g a n exists and is an integer we give an explicit way of computing such integer by proving that it equals the dimension of a suitable finite dimension semisimple g z 2 graded algebra related to a

adapted solution of a backward stochastic differential equation abstract let wt t 0 1 be a standard k dimensional weiner process defined on a probability space f p and let ft denote its natural filtration given a f1 measurable d dimensional random vector x we look for an adapted pair of processes x t y t t 0 1 with values in rd and rd k respectively which solves an equation of the form x t t 1 f s x s y s ds t 1 g s x s y s dw s x a linearized version of that equation appears in stochastic control theory as the equation satisfied by the adjoint process we also generalize our results to the following equation x t t 1 f s x s y s ds t 1 g s x s y s dw s x under rather restrictive assumptions on g

finitely generated algebras with involution and their identities abstract we consider associative algebras with involution over a field of characteristic zero in this case we prove that for any finitely generated associative algebra with involution there exists a finite dimensional algebra with involution which satisfies the same identities with involution this is an analogue and an extension of the theorem of a r kemer for ordinary identities kemer 1991 8 the similar results were proved earlier by the author for identities graded by a finite abelian group sviridova 2011 15 and by e aljadeff and a kanel belov 2010 1 for identities graded by any finite group

a characterization of minimal varieties of zp graded pi algebras abstract let f be a field of characteristic zero and p a prime in the present paper it is proved that a variety of z p graded associative pi f algebras of finite basic rank is minimal of fixed z p exponent d if and only if it is generated by an upper block triangular matrix algebra u t z p a 1 a m equipped with a suitable elementary z p grading whose diagonal blocks are isomorphic to z p graded simple algebras a 1 a m satisfying dim f a 1 a m d

on properties of stochastic inventory systems for most order quantity reorder point inventory systems the stochastic model which specifies the demands as stochastic processes is often more accurate than its deterministic counterpart the eoq model however the application of the stochastic model has been limited because of the absence of insightful analytical results on the model this paper analyzes the stochastic order quantity reorder point model in comparison with a corresponding deterministic eoq model based on simple optimality conditions for the control variables derived in the paper a sensitivity analysis is carried out and a number of basic qualitative properties are established for the optimal control parameters our main results include the following 1 in contrast to the deterministic eoq model the controllable costs of the stochastic model due to selection of the order quantity assuming the reorder point is chosen optimally for every order quantity are actually smaller while the total costs are clearly larger the optimal ord

verbally prime t ideals and graded division algebras abstract let f be an algebraically closed field of characteristic zero and let g be a finite group we consider graded verbally prime t ideals in the free g graded algebra it turns out that equivalent definitions in the ordinary case i e ungraded extend to nonequivalent definitions in the graded case namely verbally prime g graded t ideals and strongly verbally prime t ideals at first following kemer s ideas we classify g graded verbally prime t ideals the main bulk of the paper is devoted to the stronger notion we classify g graded strongly verbally prime t ideals which are t ideal of affine g graded algebras or equivalently g graded t ideals that contain a capelli polynomial it turns out that these are precisely the t ideal of g graded identities of finite dimensional g graded central over f i e z a e f which admit a g graded division algebra twisted form over a field k which contains f or equivalently over a field k which contains enough roots of unity e g a primitive n root of unity where n o r d g

group gradings on superinvolution simple superalgebras in this paper we describe all group gradings by an arbitrary finite group g on non simple finite dimensional superinvolution simple associative superalgebras over an algebraically closed field f of characteristic 0 or coprime to the order of g

group graded algebras and almost polynomial growth let f be a field of characteristic 0 g a finite abelian group and a a g graded algebra we prove that a generates a variety of g graded algebras of almost polynomial growth if and only if a has the same graded identities as one of the following algebras 1 fcp the group algebra of a cyclic group of order p where p is a prime number and p g 2 ut2g f the algebra of 2 2 upper triangular matrices over f endowed with an elementary g grading 3 e the infinite dimensional grassmann algebra with trivial g grading 4 in case 2 g ez2 the grassmann algebra with canonical z2 grading

stability of bsdes with random terminal time and homogenization of semilinear elliptic pdes in this paper we extend the probabilistic method for homogenization of semi linear parabolic pdes developed by buckdahn hu and peng to the case of elliptic pdes first we give a stability result for bsdes with random terminal time which are related to elliptic pdes as shown in peng stochastics stochastics rep 37 1991 61 74 in the one dimensional case we also partially relax the monotonicity assumption on the coefficient then we use these stability results for bsdes with random terminal time to study homogenization of systems of semilinear elliptic pdes

on double boundary non crossing probability for a class of compound processes with applications abstract we develop an efficient method for computing the probability that a non decreasing pure jump compound stochastic process stays between arbitrary upper and lower boundaries i e deterministic functions possibly discontinuous within a finite time period the compound process is composed of a process modelling the arrivals of certain events e g demands for a product in inventory systems customers in queuing or claims capital gains in insurance dual risk models and a sequence of independent and identically distributed random variables modelling the sizes of the events the events arrival process is assumed to belong to the wide class of point processes with conditional stationary independent increments which includes non homogeneous poisson binomial negative binomial mixed poisson and doubly stochastic poisson i e cox processes as special cases the proposed method is based on expressing the non exit probability through chapman kolmogorov equations re expressing them in terms of a circular convolution of two vectors which is then computed applying fast fourier transform fft we further demonstrate that our fft based method is computationally efficient and can be successfully applied in the context of inventory management to determine an optimal replenishment policy ruin theory to evaluate ruin probabilities and related quantities and double barrier option pricing or simply computing non exit probabilities for brownian motion with general boundaries

the effect of lead time and demand uncertainties in r q inventory systems we study a single item r q inventory system where r is the reorder point and q is the order quantity the demand is a compound poisson process we investigate the behavior of the optimal policy parameters and the long run average cost of the system in response to stochastically shorter or less variable lead times we show that although some of the properties of the base stock system can be extended to this more general model some cannot the same findings also apply when the comparison is conducted on the lead time demand distributions

a conjecture of regev about the capelli polynomial abstract let x1 xn2 y1 yn2 be generic n n matrices over a field k of characteristic zero if x 1 x n is a multilinear invariant of x1 xn then s z 2 sign f x 1 y 1 x 2 y 2 y 3 y 4 x 3 y 5 y 9 x n y n 2 2n 2 y n 2 f x 1 x n y where sn2 is the symmetric group of degree n2 y is the discriminant of y1 yn2 and tf x 1 x n is a uniquely defined multilinear invariant of x1 xn thus tf defines a function from the vector space of multilinear invariants of x1 xn to itself an analysis of this function is used to prove regev s conjecture that s z 2 sign x n 1 y 1 x 2 x 3 x 4 y 2 y 3 y 4 x 5 x n 2 2 2 x n 2 y n 2 2n 2 y n 2 is nonzero in addition a variant of the above function is used to evaluate the capelli polynomial

on z2 graded identities of ut2 e and their growth abstract let f be an infinite field of characteristic different from two and e be the infinite dimensional grassmann algebra over f we consider the upper triangular matrix algebra ut 2 e with entries in e endowed with the z 2 grading inherited by the natural z 2 grading of e and we study its ideal of z 2 graded polynomial identities t z 2 ideal and its relatively free algebra in particular we show that the set of z 2 graded polynomial identities of ut 2 e does not depend on the characteristic of the field moreover we compute the z 2 graded hilbert series of ut 2 e and its z 2 graded gelfand kirillov dimension

asymptotic behaviour of codimensions of p i algebras satisfying capelli identities let a be a p i algebra with 1 in characteristic zero satisfying a capelli identity then the cocharacter sequence c n a is asymptotic to a function of the form an g l n where l n and g z

linear multistep schemes for bsdes we study the convergence rate of a class of linear multistep methods for backward stochastic differential equations bsdes we show that under a sufficient condition on the coefficients the schemes enjoy a fundamental stability property coupling this result to an analysis of the truncation error allows us to design approximation with arbitrary order of convergence contrary to the analysis performed in w zhao g zhang and l ju siam j numer anal 48 2010 pp 1369 1394 we consider general diffusion models and bsdes with driver depending on z the class of methods we consider contains well known methods from the ode framework as nystrom milne or adams methods finally we provide a numerical illustration of the convergence of some methods

numerical stability analysis of the euler scheme for bsdes in this paper we study the qualitative behavior of approximation schemes for backward stochastic differential equations bsdes by introducing a new notion of numerical stability for the euler scheme we provide sufficient conditions in the one dimensional and multidimensional cases to guarantee the numerical stability we then perform a classical von neumann stability analysis in the case of a linear driver f and exhibit necessary conditions to get stability in this case finally we illustrate our results with numerical applications

on group gradings on pi algebras abstract we show that there exists a constant k such that for any pi algebra w and any nondegenerate g grading on w where g is any group possibly infinite there exists an abelian subgroup u of g with g u exp w k a g grading w g g w g is said to be nondegenerate if w g 1 w g 2 w g r 0 for any r 1 and any r tuple g 1 g 2 g r in g r

involution codimensions of finite dimensional algebras and exponential growth abstract let f be a field of characteristic zero and let a be a finite dimensional algebra with involution over f we study the asymptotic behavior of the sequence of codimensions c n a of a and we show that exp a lim n c n a exists and is an integer we give an explicit way for computing exp a and as a consequence we obtain the following characterization of simple algebras a is simple if and only if exp a dim f a

on codimension growth of finitely generated associative algebras abstract letabe a pi algebra over a fieldf we study the asymptotic behavior of the sequence of codimensionscn a ofa we show that ifais finitely generated overftheninv a limn c n a always exists and is an integer we also obtain the following characterization of simple algebras ais finite dimensional central simple overfif and only ifinv a dim a

the joint effect of leadtime variance and lot size in a parallel processing environment we study a basic r q system in which the demand is a poisson process and the leadtimes are independent identically distributed random variables the key issue is the joint effect of the leadtime variance and the lot size q on performance we know that under a simple base stock policy with q 1 the leadtime variance has no effect at all we find here that for larger q the leadtime variance can have a significant adverse impact on performance to explore this effect we test two simple approximations the simplest ignores the leadtime variance the second approach is only a bit more complex it captures the variance effect through a hybrid of two limiting approximations both methods provide useful information but the second is more robust

specht property for some varieties of jordan algebras of almost polynomial growth abstract let f be a field of characteristic zero in 25 it was proved that u j 2 the jordan algebra of 2 2 upper triangular matrices can be endowed up to isomorphism with either the trivial grading or three distinct non trivial z 2 gradings or by a z 2 z 2 grading in this paper we prove that the variety of jordan algebras generated by u j 2 endowed with any g grading has the specht property i e every t g ideal containing the graded identities of u j 2 is finitely based moreover we prove an analogue result about the ordinary identities of a 1 a suitable infinitely generated metabelian jordan algebra defined in 27

graded polynomial identities of matrices we consider g graded polynomial identities of the p p matrix algebra mp k over a field k of characteristic 0 graded by an arbitrary group g we find relations between the g graded identities of the g graded algebra mp k and the g h graded identities of the tensor product of mp k and the h graded algebra mq k with a fine h grading we also find a basis of the g graded identities of mp k with an elementary grading such that the identity component coincides with the diagonal of mp k

backward stochastic differential equations and partial differential equations with quadratic growth we provide existence comparison and stability results for one dimensional backward stochastic differential equations bsdes when the coefficient or generator f t y z is continuous and has a quadratic growth in z and the terminal condition is bounded we also give in this framework the links between the solutions of bsdes set on a diffusion and viscosity or sobolev solutions of the corresponding semilinear partial differential equations

polynomial identities and noncommutative versal torsors abstract to any cleft hopf galois object i e any algebra h obtained from a hopf algebra h by twisting its multiplication with a two cocycle we attach two universal algebras a h and u h the algebra a h is obtained by twisting the multiplication of h with the most general two cocycle formally cohomologous to the cocycle takes values in the field of rational functions on h by construction a h is a cleft h galois extension of a big commutative algebra b h any form of h can be obtained from a h by a specialization of b h and vice versa if the algebra h is simple then a h is an azumaya algebra with center b h the algebra u h is constructed using a general theory of polynomial identities that we set up for arbitrary comodule algebras it is the universal comodule algebra in which all comodule algebra identities of h are satisfied we construct an embedding of u h into a h this embedding maps the center z h of u h into b h when the algebra h is simple in this case under an additional assumption a h b h z h u h thus turning a h into a central localization of u h we completely work out these constructions in the case of the four dimensional sweedler algebra