Yangians of Lie Superalgebras
نویسنده
چکیده
This thesis is concerned with extending some well-known results about the Yangians Y (glN) and Y (slN) to the case of super-Yangians. First we produce a new presentation of the Yangian Y (glm|n), using the Gauss decomposition of a matrix with non-commuting entries. Then, by writing the quantum Berezinian in terms of generators from the new presentation we prove that its coefficients generate the centre Zm|n of Y (glm|n). We show that the Yangian Y (slm|n) is isomorphic to a subalgebra of the Yangian Y (glm|n), and in particular if m 6= n, then Y (glm|n) ∼= Zm|n ⊗ Y (slm|n). Finally, we show that a Yangian Y (psln|n) associated with the projective special linear Lie superalgebra may be obtained from Y (sln|n) by quotienting out the ideal generated by the coefficients of the quantum Berezinian.
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