TY - JOUR
T1 - On pentagon, ten-term, and tetrahedron relations
AU - Kashaev, R. M.
AU - Sergeev, S. M.
PY - 1998/7/11
Y1 - 1998/7/11
N2 - 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.
AB - 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.
KW - tetrahedron equation
UR - http://www.scopus.com/inward/record.url?scp=0001461396&partnerID=8YFLogxK
U2 - 10.1007/s002200050391
DO - 10.1007/s002200050391
M3 - Article
AN - SCOPUS:0001461396
SN - 0010-3616
VL - 195
SP - 309
EP - 319
JO - Communications in Mathematical Physics
JF - Communications in Mathematical Physics
IS - 2
ER -