摘要 :AbstractWe study graded symmetric algebras, which are the symmetric monoids in the monoidal category of vector spaces graded by a group. We show that a finite dimensional graded semisimple algebra is graded symmetric. The center o...
展开AbstractWe study graded symmetric algebras, which are the symmetric monoids in the monoidal category of vector spaces graded by a group. We show that a finite dimensional graded semisimple algebra is graded symmetric. The center of a symmetric algebra is not necessarily symmetric, but we prove that the center of a finite dimensional graded division algebra is symmetric, provided that the order of the grading group is not divisible by the characteristic of the base field.]]>
收起
摘要 :
Let F be an infinite field of characteristic p different from 2 and let E be the Grassmann algebra generated by an infinite dimensional vector space L over F. In this paper we provide, for any odd prime q, a finite basis for the T...
展开
Let F be an infinite field of characteristic p different from 2 and let E be the Grassmann algebra generated by an infinite dimensional vector space L over F. In this paper we provide, for any odd prime q, a finite basis for the T-q-ideal of the Z(q) -graded polynomial identities for E and a basis for the T-q space of graded central polynomials for E, for any Z(q)-grading on E such that L is homogeneous in the grading. Moreover, we prove that the set of all graded central polynomials of E is not finitely generated as a T-q-space, if p > 2. In the nonhomogeneous case such bases are also described when at least one non-neutral component has infinite many homogeneous elements of the basis of L in the respective grading. (C) 2020 Elsevier Inc. All rights reserved.
收起
摘要 :
Let G be an arbitrary abelian group and let A and B be two finite dimensional G-graded simple algebras over an algebraically closed field F such that the orders of all finite subgroups of G are invertible in F. We prove that A and...
展开
Let G be an arbitrary abelian group and let A and B be two finite dimensional G-graded simple algebras over an algebraically closed field F such that the orders of all finite subgroups of G are invertible in F. We prove that A and B are isomorphic if and only if they satisfy the same G-graded identities. We also describe all isomorphism classes of finite dimensional G-graded simple algebras.
收起
摘要 :
Let F be a field of characteristic 0, E be the unitary infinite dimensional Grassmann algebra over F and consider the algebra M-1,M-1 (E) with its natural Z(2)-grading. We describe the graded A-identities for M-1,M-1 (E) and we co...
展开
Let F be a field of characteristic 0, E be the unitary infinite dimensional Grassmann algebra over F and consider the algebra M-1,M-1 (E) with its natural Z(2)-grading. We describe the graded A-identities for M-1,M-1 (E) and we compute its graded A-codimensions.
收起
摘要 :
We introduce the class of extended graded Poisson algebras as a generalization of the one of graded Poisson algebras and study its structure. If P is an extended graded Poisson algebra, we show that P is of the form P=U+∑_i ~(Ii)...
展开
We introduce the class of extended graded Poisson algebras as a generalization of the one of graded Poisson algebras and study its structure. If P is an extended graded Poisson algebra, we show that P is of the form P=U+∑_i ~(Ii) with U a linear subspace of ~(P0) and any ~(Ii) a well described ideal of P, satisfying {~(Ii), ~(Ij)}+~(IiIj)=0 if i≠qj. It is also shown that, under certain conditions, P is the direct sum of the family of its simple ideals.
收起
摘要 :
We observe that a finitely generated algebraic algebra R (over a field) is finite dimensional if and only if the associated graded ring is right noetherian, if and only if has right Krull dimension, if and only if satisfies a polynomial identity.
摘要 :
Known classification results allow us to find the number of (equivalence classes of) fine gradings on matrix algebras and on classical simple Lie algebras over an algebraically closed field F (assuming char F≠2 in the Lie case). ...
展开
Known classification results allow us to find the number of (equivalence classes of) fine gradings on matrix algebras and on classical simple Lie algebras over an algebraically closed field F (assuming char F≠2 in the Lie case). The computation is easy for matrix algebras and especially for simple Lie algebras of type B_r (the answer is just r+1), but involves counting orbits of certain finite groups in the case of Series A,C and D. For X ∈ {A,C.D}, we determine the exact number of fine gradings, N_X(r), on the simple Lie algebras of type X_r with r≤100 as well as the asymptotic behavior of the average, ?_X(r), for large r. In particular, we prove that there exist positive constants b and c such that exp(br~(2/3))≤exp(cr~(2/3)). The analogous average for matrix algebras M_n (F) is proved to be a ln n+O(1) where a is an explicit constant depending on char F.
收起
摘要 :
In this survey paper we present recent classification results for gradings by arbitrary groups on finite-dimensional simple Lie algebras over an algebraically closed field of characteristic different from 2. We also describe the m...
展开
In this survey paper we present recent classification results for gradings by arbitrary groups on finite-dimensional simple Lie algebras over an algebraically closed field of characteristic different from 2. We also describe the main tools that were used to obtain these results (in particular, the classification of group gradings on matrix algebras).
收起
摘要 :
In this paper we describe all group gradings by a finite abelian group G of any Lie algebra L of the type "A" over an algebraically closed field F of characteristic zero.
摘要 :
Let F be an infinite field of characteristic different from 2, and let E be the Grassmann algebra of a countable of dimensional F-vector space L. In this paper, we study the graded central polynomials of gradings on E by the group...
展开
Let F be an infinite field of characteristic different from 2, and let E be the Grassmann algebra of a countable of dimensional F-vector space L. In this paper, we study the graded central polynomials of gradings on E by the groups Z(2) and Z, where the basis of the vector space L is homogeneous. More specifically, we provide a basis for the T-G-space of graded central polynomials for E, where the group G is Z(2) and Z.
收起
原文获取