ON Z2-GRADED IDENTITIES OF THE SUPER TENSOR PRODUCT OF UT2(F) BY THE GRASSMANN ALGEBRA

Let F be a field of characteristic zero and E be the unitary Grassmann algebra generated over an infinite-dimensional F-vector space L. Denote by E = E-(0) circle plus E-(1) an arbitrary Z(2)-grading of E such that the subspace L is homogeneous. Given a superalgebra A = A((0)) circle plus A((1)), define the superalgebra A (circle times) over cap E by A (circle times) over cap E = (A((0)) circle times E-(0)) circle plus (A((1)) circle times E-(1)). Note that when E is the canonical grading of E then A (circle times) over cap E is the Grassmann envelope of A. In this work we find bases of Z(2)-graded identities and we describe the Z(2)-graded codimension and cocharacter sequences for the superalgebras UT2(F) (circle times) over cap E, when the algebra UT2(F) of 2 x 2 upper triangular matrices over F is endowed with its canonical grading.