Classical limit of genus two DAHA
Copyright policy )Classical limit of genus two DAHA
We show that one-parameter deformation $\mathcal A_{q,t}$ of the skein algebra $Sk_q(Σ_2)$ of a genus two surface suggested in [AS19] is flat. We solve the word problem in the algebra and describe monomial basis. In addition, we calculate the classical limit $\mathcal A_{q=1,t}$ of the algebra and prove that it is a one-parameter flat Poisson deformation of the coordinate ring $\mathcal A_{q=t=1}$ of an $SL(2,\mathbb C)$-charater variety of a genus two surface. As a byproduct, we obtain a remarkably simple presentation in terms of generators and relations for the coordinate ring $\mathcal A_{q=t=1}$ of a genus two character variety.
37 pages, 1 figure
FOS: Physical sciences, Quantum groups (quantized enveloping algebras) and related deformations, Mathematics - Rings and Algebras, Mathematical Physics (math-ph), Relations of finite-dimensional Hamiltonian and Lagrangian systems with topology, geometry and differential geometry (symplectic geometry, Poisson geometry, etc.), Rings and Algebras (math.RA), 17B37, 20G42, 81R50, 37J39, Mathematics - Quantum Algebra, FOS: Mathematics, Quantum Algebra (math.QA), 2-dimensional topology (including mapping class groups of surfaces, Teichmüller theory, curve complexes, etc.), Quantum groups (quantized function algebras) and their representations, Quantum groups and related algebraic methods applied to problems in quantum theory, Mathematical Physics
FOS: Physical sciences, Quantum groups (quantized enveloping algebras) and related deformations, Mathematics - Rings and Algebras, Mathematical Physics (math-ph), Relations of finite-dimensional Hamiltonian and Lagrangian systems with topology, geometry and differential geometry (symplectic geometry, Poisson geometry, etc.), Rings and Algebras (math.RA), 17B37, 20G42, 81R50, 37J39, Mathematics - Quantum Algebra, FOS: Mathematics, Quantum Algebra (math.QA), 2-dimensional topology (including mapping class groups of surfaces, Teichmüller theory, curve complexes, etc.), Quantum groups (quantized function algebras) and their representations, Quantum groups and related algebraic methods applied to problems in quantum theory, Mathematical Physics
selected citations These citations are derived from selected sources.This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).1 popularity This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.Average influence This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).Average impulse This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.Average
Citations provided by BIP!Popularity provided by BIP!