Nichols-Woronowicz algebra model for Schubert calculus on Coxeter groups

Details Nichols-Woronowicz algebra model for Schubert calculus on Coxeter groups Nichols-Woronowicz algebra model for Schubert calculus on Coxeter groups

2004-09-13

arxiv.org/abs/math/0409206v2

J. Algebra 297 (2006), no. 2, 372--399

Mathematics

Quantum Algebra

v2: New section added where the nilCoxeter algebra is realised in the Nichols-Woronowicz algebra; switched from left to (more

Scientific paper

We realise the cohomology ring of a flag manifold, more generally the coinvariant algebra of an arbitrary finite Coxeter group W, as a commutative subalgebra of a certain Nichols algebra in the Yetter-Drinfeld category over W. This gives a braided Hopf algebra version of the corresponding Schubert calculus. Our proof is based on methods of braided differential calculus rather than on working directly with the relations in the Nichols algebra, which are not known explicitly. We also discuss the relationship between Fomin-Kirillov quadratic algebras, Kirillov-Maeno bracket algebras and our construction.

Affiliated with

Also associated with

No associations

Rating

Nichols-Woronowicz algebra model for Schubert calculus on Coxeter groups 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 Nichols-Woronowicz algebra model for Schubert calculus on Coxeter groups, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Nichols-Woronowicz algebra model for Schubert calculus on Coxeter groups will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-530844