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RESEARCH PRODUCT

A characterization of fundamental algebras through S-characters

César Polcino MiliesCésar Polcino MiliesMikhail ZaicevAntonio Giambruno

subject

Pure mathematicsPolynomialAlgebra and Number Theory010102 general mathematicsZero (complex analysis)Characterization (mathematics)01 natural sciencesSymmetric group0103 physical sciences010307 mathematical physicsFinitely-generated abelian group0101 mathematicsExterior algebraREPRESENTAÇÃO DE GRUPOS SIMÉTRICOSMathematics

description

Abstract Fundamental algebras play an important role in the theory of algebras with polynomial identities in characteristic zero. They are defined in terms of multialternating polynomials non vanishing on them. Here we give a characterization of fundamental algebras in terms of representations of symmetric groups obtaining this way an equivalent definition. As an application we determine when a finitely generated Grassmann algebra is fundamental.

yearjournalcountryeditionlanguage
2020-01-01Journal of Algebra
https://doi.org/10.1016/j.jalgebra.2019.09.005