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• W1630370186 abstract "For the last fifteen years quantum superalgebras have been used to model super-symmetric quantum systems. A class of quasi-triangular Hopf superalgebras, they each contain a universal R-matrix, which automatically satisfies the Yang-Baxter equation. Applying the vector representation to the left-hand side of a universal R-matrix gives a Lax operator. These are of significant interest in mathematical physics as they provide solutions to the Yang-Baxter equation in an arbitrary representation, which give rise to integrable models.       In this thesis a Lax operator is constructed for the quantised orthosymplectic superalgebra Uq[osp(m|n)] for all m > 2, n ≥ 2 where n is even. This can then be used to find a solution to the Yang-Baxter equation in an arbitrary representation of Uq[osp(m|n)], with the example of the vector representation given in detail.       In studying the integrable models arising from solutions to the Yang-Baxter equation, it is desirable to understand the representation theory of the superalgebra. Finding the Casimir invariants of the system and exploring their behaviour helps in this understanding. In this thesis the Lax operator is used to construct an infinite family of Casimir invariants of Uq[osp(m|n)] and to calculate their eigenvalues in an arbitrary irreducible representation." @default.
• W1630370186 created "2016-06-24" @default.
• W1630370186 creator A5051175545 @default.
• W1630370186 date "2005-01-01" @default.
• W1630370186 modified "2023-09-27" @default.
• W1630370186 title "Solutions to the Yang-Baxter equation and Casimir invariants for the quantised orthosymplectic superalgebra." @default.
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