共查询到20条相似文献,搜索用时 9 毫秒
1.
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 , n=1,2,…, the sequence of graded codimensions of A and we prove that if A satisfies an ordinary polynomial identity, 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×Z2-graded algebra related to A. 相似文献
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Let A be an algebra over a field F of characteristic zero and let cn(A), , be its sequence of codimensions. We prove that if cn(A) is exponentially bounded, its exponential growth can be any real number >1. This is achieved by constructing, for any real number α>1, an F-algebra Aα such that exists and equals α. The methods are based on the representation theory of the symmetric group and on properties of infinite Sturmian and periodic words. 相似文献
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A non-nilpotent variety of algebras is almost nilpotent if any proper subvariety is nilpotent. Let the base field be of characteristic zero. It has been shown that for associative or Lie algebras only one such variety exists. Here we present infinite families of such varieties. More precisely we shall prove the existence of1) a countable family of almost nilpotent varieties of at most linear growth and2) an uncountable family of almost nilpotent varieties of at most quadratic growth. 相似文献
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We classify, up to PI-equivalence, the superalgebras over a field of characteristic zero whose sequence of codimensions is linearly bounded. As a consequence we determine the linear functions describing the graded codimensions of a superalgebra. 相似文献
6.
Karin Erdmann 《Journal of Pure and Applied Algebra》2011,215(2):185-200
One of our main results is a classification of all the weakly symmetric radical cube zero finite dimensional algebras over an algebraically closed field having a theory of support via the Hochschild cohomology ring satisfying Dade’s Lemma. In the process we give a characterization of when a finite dimensional Koszul algebra has such a theory of support in terms of the graded centre of the Koszul dual. 相似文献
7.
We study prime monomial algebras. Our main result is that a prime finitely presented monomial algebra is either primitive or it has GK dimension one and satisfies a polynomial identity. More generally, we show that this result holds for the class of automaton algebras; that is, monomial algebras that have a basis consisting of the set of words recognized by some finite state automaton. This proves a special case of a conjecture of the first author and Agata Smoktunowicz. 相似文献
8.
Lucio Centrone 《Journal of Pure and Applied Algebra》2019,223(7):2977-2996
We prove a strict relation between the Gelfand–Kirillov (GK) dimension of the relatively free (graded) algebra of a PI-algebra and its (graded) exponent. As a consequence we show a Bahturin–Zaicev type result relating the GK dimension of the relatively free algebra of a graded PI-algebra and the one of its neutral part. We also get that the growth of the relatively free graded algebra of a matrix algebra is maximal when the grading is fine. Finally we compute the graded GK dimension of the matrix algebra with any grading and the graded GK dimension of any verbally prime algebra endowed with an elementary grading. 相似文献
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Karin Erdmann 《Journal of Pure and Applied Algebra》2011,215(7):1747-1768
One of our main results is a classification of all the possible quivers of selfinjective radical cube zero finite-dimensional algebras over an algebraically closed field having finite complexity. In the paper (Erdmann and Solberg, 2011) [5] we classified all weakly symmetric algebras with support varieties via Hochschild cohomology satisfying Dade’s Lemma. For a finite-dimensional algebra to have such a theory of support varieties implies that the algebra has finite complexity. Hence this paper is a partial extension of [5]. 相似文献
12.
Agata Smoktunowicz 《Journal of Pure and Applied Algebra》2007,209(3):839-851
It is shown that for every countable field K, there is a finitely generated graded Jacobson radical algebra over K of Gelfand-Kirillov dimension two. Examples of finitely generated Jacobson radical algebras of Gelfand-Kirillov dimension two over algebraic extensions of finite fields of characteristic 2 were earlier constructed by Bartholdi [L. Bartholdi, Branch Rings, thinned rings, tree enveloping rings, Israel J. Math. (in press)]. 相似文献
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Petter Andreas Bergh 《Journal of Pure and Applied Algebra》2008,212(4):753-773
We define and study twisted support varieties for modules over an Artin algebra, where the twist is induced by an automorphism of the algebra. Under a certain finite generation hypothesis we show that the twisted variety of a module satisfies Dade’s Lemma and is one dimensional precisely when the module is periodic with respect to the twisting automorphism. As a special case we obtain results on DTr-periodic modules over Frobenius algebras. 相似文献
14.
David J. Benson 《Journal of Pure and Applied Algebra》2007,211(2):497-510
We develop a rank variety for finite-dimensional modules over a certain class of finite-dimensional local k-algebras, . Included in this class are the truncated polynomial algebras , with k an algebraically closed field and arbitrary. We prove that these varieties characterise projectivity of modules (Dade’s lemma) and examine the implications for the tree class of the stable Auslander-Reiten quiver. We also extend our rank varieties to infinitely generated modules and verify Dade’s lemma in this context. 相似文献
15.
Ping-Bao Liao 《Linear algebra and its applications》2009,430(4):1236-197
Let A be a prime algebra of characteristic not 2 with extended centroid C, let R be a noncentral Lie ideal of A and let B be the subalgebra of A generated by R. If f,d:R→A are linear maps satisfying that
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Miles Holloway 《Archiv der Mathematik》2008,90(4):311-316
We answer a question raised in [9] by showing the equality of two different definitions of rank variety for finitely generated
modules over truncated polynomial algebras. We do this by establishing an isomorphism of algebras used in the two definitions
of rank variety.
Received: 23 April 2007 相似文献
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We describe how to calculate the (, )-minimal sets in any finite ring. 相似文献
18.
We study associative algebras with 1 endowed with an automorphism or antiautomorphism φ of order 2, i.e., superalgebras and algebras with involution. For any fixed k≥1, we construct associative φ-algebras whose φ-codimension sequence is given asymptotically by a polynomial of degree k whose leading coefficient is the largest or smallest possible. 相似文献
19.
Claus Michael Ringel 《Journal of Pure and Applied Algebra》2010,214(9):1687-1692
Let Λ be an artin algebra and X a finitely generated Λ-module. Iyama has shown that there exists a module Y such that the endomorphism ring Γ of X⊕Y is quasi-hereditary, with a heredity chain of length n, and that the global dimension of Γ is bounded by this n. In general, one only knows that a quasi-hereditary algebra with a heredity chain of length n must have global dimension at most 2n−2. We want to show that Iyama’s better bound is related to the fact that the ring Γ he constructs is not only quasi-hereditary, but even left strongly quasi-hereditary. By definition, the left strongly quasi-hereditary algebras are the quasi-hereditary algebras with all standard left modules of projective dimension at most 1. 相似文献
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