Search results for "Graded algebras"

Gradings on the algebra of upper triangular matrices of size three

2013

Abstract Let UT 3 ( F ) be the algebra of 3 × 3 upper triangular matrices over a field F . On UT 3 ( F ) , up to isomorphism, there are at most five non-trivial elementary gradings and we study the graded polynomial identities for such gradings. In case F is of characteristic zero we give a complete description of the space of multilinear graded identities in the language of Young diagrams through the representation theory of a Young subgroup of S n . We finally compute the multiplicities in the graded cocharacter sequence for every elementary G -grading on UT 3 ( F ) .

ALGEBRE SIMMETRICHE DI ALCUNE CLASSI DI IDEALI MONOMIALI

The purpose of this thesis is the study of the symmetric algebra 〖Sym〗_S (L) of an interesting class of monomial ideals: the ideals L ⊂S=K[x1,...,xn,y1,...,ym] of mixed products in two sets of variables. Recently, this class is been used in order to test some algebraic conjecture, including the conjecture of Eisenbud -Goto, on the symmetric algebra 〖Sym〗_S (L) .Since such conjecture involves fundamental invariants of Sym (L), such as the Krull dimension, the multiplicity and regularity of Castelnuovo-Mumford, it was necessary to calculate these invariants or their bounds. This problem is difficult, but if L is generated by a s-sequence, you can arrive at a concrete result. In the work Mixed…

Classifying G-graded algebras of exponent two

2019

Let F be a field of characteristic zero and let $$\mathcal{V}$$ be a variety of associative F-algebras graded by a finite abelian group G. If $$\mathcal{V}$$ satisfies an ordinary non-trivial identity, then the sequence $$c_n^G(\mathcal{V})$$ of G-codimensions is exponentially bounded. In [2, 3, 8], the authors captured such exponential growth by proving that the limit $$^G(\mathcal{V}) = {\rm{lim}}_{n \to \infty} \sqrt[n]{{c_n^G(\mathcal{V})}}$$ exists and it is an integer, called the G-exponent of $$\mathcal{V}$$ . The purpose of this paper is to characterize the varieties of G-graded algebras of exponent greater than 2. As a consequence, we find a characterization for the varieties with …

Group graded algebras and multiplicities bounded by a constant

2013

AbstractLet 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.