Algebraic Structures on Grothendieck Groups of a Tower of Algebras

Details Algebraic Structures on Grothendieck Groups of a Tower of Algebras Algebraic Structures on Grothendieck Groups of a Tower of Algebras

2006-12-06

arxiv.org/abs/math/0612170v1

J. Algebra 321 (2009), no. 8, 2068-2084

Mathematics

Rings and Algebras

Scientific paper

The Grothendieck group of the tower of symmetric group algebras has a self-dual graded Hopf algebra structure. Inspired by this, we introduce by way of axioms, a general notion of a tower of algebras and study two Grothendieck groups on this tower linked by a natural paring. Using representation theory, we show that our axioms give a structure of graded Hopf algebras on each Grothendieck groups and these structures are dual to each other. We give some examples to indicate why these axioms are necessary. We also give auxiliary results that are helpful to verify the axioms. We conclude with some remarks on generalized towers of algebras leading to a structure of generalized bialgebras (in the sense of Loday) on their Grothendieck groups.

Affiliated with

Also associated with

No associations

Rating

Algebraic Structures on Grothendieck Groups of a Tower of Algebras does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Algebraic Structures on Grothendieck Groups of a Tower of Algebras, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Algebraic Structures on Grothendieck Groups of a Tower of Algebras will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-16275