Projects per year
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.
|Number of pages||29|
|Journal||Linear algebra and its applications|
|Early online date||6 Feb 2018|
|Publication status||Published - 1 Jun 2018|
FingerprintDive into the research topics of 'Set-theoretic solutions of the Yang-Baxter equation and new classes of R-matrices'. Together they form a unique fingerprint.
- 1 Finished
Combinatorial methods in noncommutative ring theory (COIMBRA)
1/06/13 → 31/05/18