Kozybaev, DaniyarUmirbaev, UalbaiZhelyabin, Viktor
23页
查看更多>>摘要：Locally finiteness of some varieties of nonassociative coalgebras is studied and the Gelfand-Dorfman construction for Novikov coalgebras and the Kantor construction for Jordan super-coalgebras are given. We give examples of a non-locally finite differential coalgebra, Novikov coalgebra, Lie coalgebra, Jordan super-coalgebra, and right-alternative coalgebra. The dual algebra of each of these examples satisfies very strong additional identities. We also constructed examples of an infinite dimensional simple differential coalgebra, Novikov coalgebra, Lie coalgebra, and Jordan super-coalgebra over a field of characteristic zero.(c) 2022 Elsevier Inc. All rights reserved.
查看更多>>摘要：Let G be a group and F an infinite field. Assume that A is a finite dimensional F-algebra with an elementary G grading. In this paper, we study the graded identities satisfied by the tensor product grading on the F-algebra A circle times C, where C is an H-graded colour beta-commutative algebra. More precisely, under a technical condition, we provide a basis for the T-G-ideal of graded polynomial identities of A circle times C, up to graded monomial identities. Furthermore, the F-algebra of upper block-triangular matrices UT(d(1), . . . , d(n)), as well as the matrix algebra M-n(F), with an elementary grading such that the neutral component corresponds to its diagonal, are studied. As a consequence of our results, a basis for the graded identities, up to graded monomial identities of degrees <= 2d - 1, for M-d(E) and M-q(F) circle times UT(d(1), ... , d(n)), with a tensor product grading, is exhibited. In this latter case, d = d(1) + . . . + d(n). Here E denotes the infinite dimensional Grassmann algebra with its natural Z(2)-grading, and the grading on M-q(F) is Pauli grading. The results presented in this paper generalize results from [14] and from other papers which were obtained for fields of characteristic zero. (c) 2022 Published by Elsevier Inc.
NSTL
Elsevier