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.