On pentagon, ten-term, and tetrahedron relations

R. M. Kashaev, S. M. Sergeev

Research output: Contribution to journalArticle

12 Citations (Scopus)

Abstract

It is shown that the tetrahedron equation under the substitution R123 = S̄13P23S13, where P23 is the permutation operator, is reduced to a pair of pentagon and one ten-term equations on operators S and S̄. Examples of infinite dimensional solutions are found. O-doubles of Novikov, which generalize the Heisenberg double of a Hopf algebra, provide a particular algebraic solution to the problem.

Original languageEnglish
Pages (from-to)309-319
Number of pages11
JournalCommunications in Mathematical Physics
Volume195
Issue number2
DOIs
Publication statusPublished - 11 Jul 1998
Externally publishedYes

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Pentagon
Triangular pyramid
tetrahedrons
operators
permutations
Term
Operator
Hopf Algebra
Substitution
Permutation
algebra
substitutes
Generalise

Cite this

Kashaev, R. M. ; Sergeev, S. M. / On pentagon, ten-term, and tetrahedron relations. In: Communications in Mathematical Physics. 1998 ; Vol. 195, No. 2. pp. 309-319.
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On pentagon, ten-term, and tetrahedron relations. / Kashaev, R. M.; Sergeev, S. M.

In: Communications in Mathematical Physics, Vol. 195, No. 2, 11.07.1998, p. 309-319.

Research output: Contribution to journalArticle

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