Elliptic Quantum Groups U_q,p(gl_N) and E_q,p(gl_N)

2016/03/14 by Hitoshi Konno, Konno, Hitoshi
Mathematics · #17B37 #20G42 #81R10 #81R50 #Advanced Topics in Algebra #Algebraic Geometry (math.AG) #Algebraic structures and combinatorial models #FOS: Mathematics #FOS: Physical sciences #High Energy Physics - Theory (hep-th) #Homotopy and Cohomology in Algebraic Topology #Mathematical Physics (math-ph) #Quantum Algebra (math.QA) #Representation Theory (math.RT)

paper · pdf · doi:10.48550/arxiv.1603.04129

openalex publication_date 2016/03/14 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We reformurate a central extension of Felder's elliptic quantum group in the FRST formulation as a topological algebra E_q,p(gl_N) over the ring of formal power series in p. We then discuss the isomorphism between E_q,p(gl_N) and the elliptic algebra U_q,p(gl_N) of the Drinfeld realization. An evaluation H-algebra homomorphism from U_q,p(gl_N) to a dynamical extension of the quantum affine algebra U_q(gl_N) resolves the problem into the one discussed by Ding and Frenkel in the trigonometric case. We also provide some useful formulas for the elliptic quantum determinants.

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