On pentagon, ten-term, and tetrahedron relations

1996/07/30 by Kashaev, R. M., Sergeev, S. M. · 4 citations
#FOS: Mathematics #Quantum Algebra (math.QA)

paper · doi:10.48550/arxiv.q-alg/9607032

Abstract

The tetrahedron equation in a special substitution is reduced to a pair of pentagon and one ten-term equations. Various examples of solutions are found. O-doubles of Novikov, which generalize the Heisenberg double of a Hopf algebra, provide a particular algebraic solution to the problem.

Cited by

• Quantum Dilogarithms and New Integrable Lattice Models in Three Dimensions
• Constructing solutions of simplex equations from polygon equations
• On an analogue of Frobenius formalism for 3-algebras and pentagon equations solutions arising from projectors
• Associative Pentagon Algebras

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