V.N. Karazin Kharkiv National University,

4 Svoboda Sq.,

61077 Kharkov,

UKRAINE

E-mail: Steven.A.Duplij@univer.kharkov.ua, kotulska@mail.ru, a.sadovnikov@inbox.ru

**Constant solutions of quantum Yang-Baxter equation
and R-matrix over Grassmann algebra**

**Abstract:**

Constant solutions to Yang-Baxter equation are investigated for the
case of 6-vertex *R*-matrix which appears in description of exactly
solvable models, quantum plane and special quantum gates. The general classification
of all possible solutions over Grassmann algebra and particular cases are
studied. As distinct from the

standard case, when *R*-matrix can have only 5 elements, we obtained
full 6-vertex solution. The solutions leading to regular *R*-matrices
which appear in weak Hopf algebras are considered.