208 research outputs found
Set-theoretic solutions of the Yang-Baxter equation and new classes of R-matrices
We describe several methods of constructing R-matrices that are dependent
upon many parameters, for example unitary R-matrices and R-matrices whose
entries are functions. As an application, we construct examples of R-matrices
with prescribed singular values.
We characterise some classes of indecomposable set-theoretic solutions of the
quantum Yang-Baxter equation (QYBE) and construct R-matrices related to such
solutions. In particular, we establish a correspondence between one-generator
braces and indecomposable, non-degenerate involutive set-theoretic solutions of
the QYBE, showing that such solutions are abundant.
We show that R-matrices related to involutive, non-degenerate solutions of
the QYBE have special form.
We also investigate some linear algebra questions related to R-matrices.Comment: Corrected typos and improved presentatio
JACOBSON RADICAL ALGEBRAS WITH QUADRATIC GROWTH
AbstractWe show that over every countable algebraically closed field there exists a finitely generated -algebra that is Jacobson radical, infinite-dimensional, generated by two elements, graded and has quadratic growth. We also propose a way of constructing examples of algebras with quadratic growth that satisfy special types of relations.</jats:p
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