(δ,ε)(\delta,\varepsilon)-Differential Identities of UTm(F)UT_m(F)

Let δ and ε be the inner derivations of UT m(F) induced by the unit matrices e 1m and e mm respectively. We study the differential polynomial identities of the algebra UT m(F) under the coupled action of δ and ε. We produce a basis of the differential identities, then we determine the S n-structure of their proper multilinear spaces and, for the minimal cases m = 2, 3, their exact differential codimension sequence

Graded Polynomial Identities of Triangular Algebras

Let F be any field, G a finite abelian group and let A, B be F-algebras graded by subgroups of G. If M is a G-graded free (A, B)-bimodule, we describe the G-graded polynomial identities of the triangular algebra of M and, in case the field F has characteristic zero, we provide the description of its G-graded cocharacters by means of the graded cocharacters of A and B

Z2-graded cocharacters for superalgebras of triangular matrices

AbstractLet K be a field of characteristic zero, let A, B be K-algebras with polynomial identity and let M be a free (A,B)-bimodule. The algebra R=A0MB can be endowed with a natural Z2-grading. In this paper, we compute the graded cocharacter sequence, the graded codimension sequence and the superexponent of R. As a consequence of these results, we also study the above PI-invariants in the setting of upper triangular matrices. In particular, we completely classify the algebra of 3×3 upper triangular matrices endowed with all possible Z2-gradings

ON THE EXISTENCE OF THE GRADED EXPONENT FOR FINITE DIMENSIONAL MATHBBZPMATHBB{Z}_P-GRADED ALGEBRAS

Let F be an algebraically closed field of characteristic zero, and let A be an associative unitary F-algebra graded by a group of prime order. We prove that if A is finite dimensional then the graded exponent of A exists and is an integer

Comparing the Z_2-Graded Identities of Two Minimal Superalgebras with the Same Superexponent

Let F be a field of characteristic zero. We study two minimal superalgebras A and B having the same superexponent but such that T2(A) â«\u8b T2(B), thus providing the first example of a minimal superalgebra generating a non minimal supervariety. We compare the structures and codimension sequences of A and B

Differential Polynomial Identities of Upper Triangular Matrices Under the Action of the Two-Dimensional Metabelian Lie Algebra

AbstractWe study the differential polynomial identities of the algebra UTm(F) under the derivation action of the two dimensional metabelian Lie algebra, obtaining a generating set of the TL-ideal they constitute. Then we determine the Sn-structure of their proper multilinear spaces and, for the minimal cases m = 2, 3, their exact differential codimension sequence.</jats:p