2025/05/21 by Rinat Kashaev, Kashaev, Rinat, Vladimir V. Mangazeev +1
Computer Science · Mathematics · #16T05 (Primary) 16T25 #16T30 #57K10 #57K14 (Secondary) #Advanced Algebra and Logic #Advanced Topics in Algebra #Algebraic structures and combinatorial models #FOS: Mathematics #FOS: Physical sciences #Geometric Topology (math.GT) #Mathematical Physics (math-ph) #Quantum Algebra (math.QA) #Rings and Algebras (math.RA)
paper · pdf · doi:10.48550/arxiv.2505.15569
openalex publication_date 2025/05/21 · openalex created_date 2025/10/19 · openalex updated_date 2026/08/03
We show that the exterior algebra of a vector space V of dimension greater than one admits a one-parameter family of braided Hopf algebra structures, arising from its identification with a Nichols algebra. We explicitly compute the structure constants with respect to a natural set-theoretic basis. A one-parameter family of diagonal automorphisms exists, which we use to construct solutions to the (constant) Yang--Baxter equation. These solutions are conjectured to give rise to the two-variable Links--Gould polynomial invariants associated with the super-quantum group Uq(\mathfrakgl(N|1)), where N = dim(V). We support this conjecture through computations for small values of N.