Graded A-identities for the matrix algebra of order two
| Autor: | Plamen Koshlukov, Antônio Pereira Brandão, Dimas José Gonçalves |
|---|---|
| Rok vydání: | 2016 |
| Předmět: |
Hilbert series and Hilbert polynomial
Computer Science::Information Retrieval General Mathematics 010102 general mathematics Astrophysics::Instrumentation and Methods for Astrophysics Graded ring Parity of a permutation Alternating group Computer Science::Computation and Language (Computational Linguistics and Natural Language and Speech Processing) 010103 numerical & computational mathematics 01 natural sciences Superalgebra Graded Lie algebra Combinatorics Filtered algebra symbols.namesake TheoryofComputation_MATHEMATICALLOGICANDFORMALLANGUAGES Differential graded algebra ComputingMethodologies_SYMBOLICANDALGEBRAICMANIPULATION ComputingMethodologies_DOCUMENTANDTEXTPROCESSING symbols Computer Science::General Literature 0101 mathematics ComputingMilieux_MISCELLANEOUS Mathematics |
| Zdroj: | International Journal of Algebra and Computation. 26:1617-1631 |
| ISSN: | 1793-6500 0218-1967 |
| DOI: | 10.1142/s0218196716500715 |
| Popis: | Let [Formula: see text] be a field of characteristic 0 and let [Formula: see text]. The algebra [Formula: see text] admits a natural grading [Formula: see text] by the cyclic group [Formula: see text] of order 2. In this paper, we describe the [Formula: see text]-graded A-identities for [Formula: see text]. Recall that an A-identity for an algebra is a multilinear polynomial identity for that algebra which is a linear combination of the monomials [Formula: see text] where [Formula: see text] runs over all even permutations of [Formula: see text] that is [Formula: see text], the [Formula: see text]th alternating group. We first introduce the notion of an A-identity in the case of graded polynomials, then we describe the graded A-identities for [Formula: see text], and finally we compute the corresponding graded A-codimensions. |
| Databáze: | OpenAIRE |
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