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 ℤZ2-graded Hilbert series of UT2(E) and its ℤZ2-graded Gelfand-Kirillov dimension.
On ℤ2-graded identities of UT 2 (E) and their growth
Centrone L.;
2015-01-01
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 ℤZ2-graded Hilbert series of UT2(E) and its ℤZ2-graded Gelfand-Kirillov dimension.File in questo prodotto:
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