Finite-dimensional simple graded algebras

Bahturin, Yuri; Zaicev, Mikhail; Sehgal, Sudarshan K.

doi:10.1070/sm2008v199n07abeh003949

Cited by 56 publications

(56 citation statements)

References 20 publications

Supporting

Mentioning

Contrasting

Unclassified

Order By: Relevance

“…Now by [15], E generate a variety of algebras of almost polynomial growth and, by [21], E Z 2 generates a variety of Z 2 -graded of almost polynomial growth. Reading this result in terms of Ggradings we get In what follows we shall need the description of finite dimensional G-graded simple algebras given in [4]. It should be mentioned that this result holds for arbitrary groups (and not only for finite abelian groups).…”

Section: Proposition 5 If G Is Any Group U T G 2 Generates a Varietmentioning

confidence: 93%

Group graded algebras and almost polynomial growth

Valenti¹

2011

Journal of Algebra

View full text Add to dashboard Cite

Let F be a field of characteristic 0, G a finite abelian group and A a\ud G-graded algebra. We prove that A generates a variety of G-graded\ud algebras of almost polynomial growth if and only if A has the same\ud graded identities as one of the following algebras:\ud (1) FCp , the group algebra of a cyclic group of order p, where p\ud is a prime number and p | |G|;\ud (2) UTG\ud 2 (F ), the algebra of 2×2 upper triangular matrices over F\ud endowed with an elementary G-grading;\ud (3) E, the infinite dimensional Grassmann algebra with trivial Ggrading;\ud (4) in case 2 | |G|, EZ2 , the Grassmann algebra with canonical Z2-\ud grading

show abstract

Section: Proposition 5 If G Is Any Group U T G 2 Generates a Varietmentioning

confidence: 93%

Group graded algebras and almost polynomial growth

Valenti¹

2011

Journal of Algebra

View full text Add to dashboard Cite

show abstract

“…Another basic ingredient we shall need is the following theorem of Bahturin et al [5] that gives a characterization of the G × Z 2 -simple algebras. …”

Section: Preliminariesmentioning

confidence: 99%

Group graded algebras and multiplicities bounded by a constant

Cirrito¹,

Giambruno²

2013

Journal of Pure and Applied Algebra

View full text Add to dashboard Cite

a b s t r a c tLet G be a finite group and A a G-graded algebra over a field of characteristic zero. When A is a PI-algebra, the graded codimensions of A are exponentially bounded and one can study the corresponding graded cocharacters via the representation theory of products of symmetric groups. Here we characterize in two different ways when the corresponding multiplicities are bounded by a constant.

show abstract

“…Further, the hypothesis on the group G is more general than the hypothesis in [9]. In fact, in [9] the hypothesis that the orders of all finite subgroups of G must be invertible in F, comes from the description of all graded simple associative algebras, according to [2,Theorems 2 and 3]. We note that no classification is used here.…”

Section: Introductionmentioning

confidence: 99%