A basis for the quantum algebra of type E6
DOI:
https://doi.org/10.35819/remat2025v11id7505Keywords:
PBW-basis, quantum groups, Hopf algebrasAbstract
Quantum algebras, or quantum groups, are non-commutative and non-cocommutative Hopf algebras. In this work we consider the infinite-dimensional quantum enveloping algebra obtained from the simple Lie algebra of type E6. Initially, we make the complete construction of this algebra based on the characteristics of the Lie algebra, which can be obtained from its Cartan matrix. Once the generators, relations and quantization parameters of the algebra are obtained, the purpose is to construct its PBW base, which is extremely important in many tools used in the study of Hopf algebras, such as, for example, the determination of coideal subalgebras, the calculation of the combinatorial rank and even the study of its representations.
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Copyright (c) 2025 Bárbara Pogorelsky, Vitória Gomes
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