On the Combinatorics of the Universal Enveloping Algebra Uh(sl2)
Rafael Diaz, Edward Salamanca
TL;DR
This paper explores the combinatorial structure of the universal enveloping algebra Uh(sl2), providing explicit formulas and combinatorial models for its elements' products.
Contribution
It introduces explicit combinatorial formulas and objects for understanding the product structure in Uh(sl2), advancing algebraic combinatorics.
Findings
Explicit product formulas for Uh(sl2) elements
Construction of combinatorial objects representing algebraic operations
Enhanced understanding of Uh(sl2) structure
Abstract
We study using combinatorial methods the structural coefficients of the formal homogeneous universal enveloping algebra Uh(sl2) of the special linear algebra sl2 over a field of characteristic zero. We provide explicit formulae for the product of generic elements in Uh(sl2), and construct combinatorial objects giving flesh to these formulae.
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Taxonomy
TopicsAdvanced Topics in Algebra · Algebraic structures and combinatorial models · Advanced Combinatorial Mathematics