ON THE QUANTUM STUCTURE OF THE UNIVERSAL ENVELOPING ALGEBRA OF THE LIE ALGEBRA ST (2)
Vol. 24 No. 92 (2000), Mathematics
Vol. 24 No. 92 (2000)

ON THE QUANTUM STUCTURE OF THE UNIVERSAL ENVELOPING ALGEBRA OF THE LIE ALGEBRA ST (2)

Mathematics
https://doi.org/10.18257/raccefyn.24(92).2000.2743
Published 2024-07-31
Berenice Guerrero
Departamento de Matemáticas y Estadística, Universidad Nacional de Colombia, Bogotá
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How to Cite

Guerrero, B. (2024). ON THE QUANTUM STUCTURE OF THE UNIVERSAL ENVELOPING ALGEBRA OF THE LIE ALGEBRA ST (2). Revista De La Academia Colombiana De Ciencias Exactas, Físicas Y Naturales, 24(92), 427–434. https://doi.org/10.18257/raccefyn.24(92).2000.2743
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Abstract

The structure of Hopf co-Poisson algebra on the universal enveloping algebra U(S7(2)) of Lie algebra S7(2) is determined with the help of a solution of the Yang-Baxter equation. Using this solution, a bracket on the dual space of Lie algebra ST(2) is also determined. This cobracket on ST(2) induces a deformation of the universal enveloping algebra U(S7(2)) which has a Hopf algebra structure, as we shall verify. This Hopf algebra is called the quantum group associated to a universal enveloping algebra.

https://doi.org/10.18257/raccefyn.24(92).2000.2743

Keywords

Lie bialgebras | Hopf algebras | Poisson brackets | Lie Poisson group | Hopf co-Poisson algebra | Universal enveloping algebra | r-matrix | Quantum group | Yang-Baxter equation
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