The primitives and antipode in the Hopf algebra of symmetric functions in noncommuting variables
Aaron Lauve, Mitja Mastnak
TL;DR
This paper explores the structure of the Hopf algebra NCSym of symmetric functions in noncommuting variables, identifying primitive elements and providing a combinatorial formula for the antipode.
Contribution
It introduces a set of primitive elements generating NCSym and derives a combinatorial formula for its antipode, advancing understanding of its algebraic structure.
Findings
Primitive elements generating NCSym identified
Combinatorial antipode formula derived
Enhanced understanding of noncommutative symmetric functions
Abstract
We identify a collection of primitive elements generating the Hopf algebra NCSym of symmetric functions in noncommuting variables and give a combinatorial formula for the antipode.
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