Abstract
Let F be an infinite field of characteristic different from two and E be the infinite dimensional Grassmann algebra over F. We consider the upper triangular matrix algebra UT2(E) with entries in E endowed with the Z2-grading inherited by the natural Z2-grading of E and we study its ideal of Z2-graded polynomial identities (TZ2-ideal) and its relatively free algebra. In particular we show that the set of Z2-graded polynomial identities of UT2(E) does not depend on the characteristic of the field. Moreover we compute the Z2-graded Hilbert series of UT2(E) and its Z2-graded Gelfand–Kirillov dimension.
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