Commutative subalgebras of the Grassmann algebra-Reference-Cited by-同舟云学术

Commutative subalgebras of the Grassmann algebra

Published:2015-04-27 Issue:08 Volume:14 Page:1550125
ISSN:0219-4988
Container-title:Journal of Algebra and Its Applications
language:en
Short-container-title:J. Algebra Appl.

Author:

Domokos M.¹,Zubor M.²

Affiliation:

1. Rényi Institute of Mathematics, Hungarian Academy of Sciences, 1053 Budapest, Reáltanoda utca 13-15, Hungary

2. Department of Algebra, Budapest University of Technology and Economics, 1521 Budapest, P. O. Box 91, Hungary

Abstract

The maximal dimension of a commutative subalgebra of the Grassmann algebra is determined. It is shown that for any commutative subalgebra there exists an equidimensional commutative subalgebra spanned by monomials. It follows that the maximal dimension of a commutative subalgebra can be expressed in terms of the maximal size of an intersecting system of subsets of odd size in a finite set.

Publisher

World Scientific Pub Co Pte Lt

Subject

Applied Mathematics,Algebra and Number Theory

Link

https://www.worldscientific.com/doi/pdf/10.1142/S021949881550125X

Reference7 articles.

1. Gotzmann Theorems for Exterior Algebras and Combinatorics

2. The jacobian map, the jacobian group and the group of automorphisms of the Grassmann algebra

3. INTERSECTION THEOREMS FOR SYSTEMS OF FINITE SETS

4. On maximal commutative algebras of linear transformations

5. Schur’s theorems on commutative matrices

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