A Characterization of Symmetric and Exterior Algebras in Characteristic Zero

Reynir Axelsson, Jón Magnússon

Research output: Contribution to journalArticlepeer-review

Abstract

We prove that a commutative (resp. modified anticommutative) connected graded Hopf algebra over a commutative algebra over a field of characteristic zero is a symmetric algebra (resp. exterior algebra) if and only if it satisfies a certain “codistributive law”, expressed by a commutative diagram. Both results are obtained as a corollary of an analogous characterization of the symmetric superalgebra of a supermodule over a superring: The symmetric superalgebras over a superring R in characteristic zero are exactly the comodules over the symmetric superalgebra of R.

Original languageEnglish
Pages (from-to)631-638
Number of pages8
JournalCommunications in Algebra
Volume20
Issue number3
DOIs
Publication statusPublished - Jan 1992

Other keywords

  • . Superalgebra
  • exterior algebra
  • graded Hopf algebra. 1980 Mathematics subject classifications 16A24 15A75 15A78
  • symmetric algebra

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