Maximal commutative subalgebras of a Grassmann algebra

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We provide a new approach to the investigation of maximal commutative subalgebras (with respect to inclusion) of Grassmann algebras. We show that finding a maximal commutative subalgebra in Grassmann algebras is equivalent to constructing an intersecting family of subsets of various odd sizes in [n] which satisfies certain combinatorial conditions. Then we find new maximal commutative subalgebras in the Grassmann algebra of odd rank n by constructing such combinatorial systems for odd n. These constructions provide counterexamples to conjectures made by Domoskos and Zubor.

Original languageEnglish
Article number1950139
JournalJournal of Algebra and its Applications
Issue number7
Publication statusPublished - Jul 1 2019


  • Grassmann algebra
  • exterior algebra
  • maximal commutative subalgebra

ASJC Scopus subject areas

  • Algebra and Number Theory
  • Applied Mathematics


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