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Defining relations for quantum symmetric pair coideals of Kac-Moody type

Hadewijch De Clercq
(2021) JOURNAL OF COMBINATORIAL ALGEBRA. 5(4). p.297-367
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Abstract
Classical symmetric pairs consist of a symmetrizable Kac-Moody algebra g, together with its subalgebra of fixed points under an involutive automorphism of the second kind. Quantum group analogs of this construction, known as quantum symmetric pairs, replace the fixed point Lie subalgebras by one-sided coideal subalgebras of the quantized enveloping algebra U_q(g). We provide a complete presentation by generators and relations for these quantum symmetric pair coideal subalgebras. These relations are of inhomogeneous q-Serre type and are valid without restrictions on the generalized Cartan matrix. We draw special attention to the split case, where the quantum symmetric pair coideal subalgebras are generalized q-Onsager algebras.
Keywords
Quantum groups, Kac-Moody algebras, quantum symmetric pairs, coideal subalgebras, q-Onsager algebra, Serre presentation, Dolan-Grady relations

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MLA
De Clercq, Hadewijch. “Defining Relations for Quantum Symmetric Pair Coideals of Kac-Moody Type.” JOURNAL OF COMBINATORIAL ALGEBRA, vol. 5, no. 4, 2021, pp. 297–367, doi:10.4171/JCA/57.
APA
De Clercq, H. (2021). Defining relations for quantum symmetric pair coideals of Kac-Moody type. JOURNAL OF COMBINATORIAL ALGEBRA, 5(4), 297–367. https://doi.org/10.4171/JCA/57
Chicago author-date
De Clercq, Hadewijch. 2021. “Defining Relations for Quantum Symmetric Pair Coideals of Kac-Moody Type.” JOURNAL OF COMBINATORIAL ALGEBRA 5 (4): 297–367. https://doi.org/10.4171/JCA/57.
Chicago author-date (all authors)
De Clercq, Hadewijch. 2021. “Defining Relations for Quantum Symmetric Pair Coideals of Kac-Moody Type.” JOURNAL OF COMBINATORIAL ALGEBRA 5 (4): 297–367. doi:10.4171/JCA/57.
Vancouver
1.
De Clercq H. Defining relations for quantum symmetric pair coideals of Kac-Moody type. JOURNAL OF COMBINATORIAL ALGEBRA. 2021;5(4):297–367.
IEEE
[1]
H. De Clercq, “Defining relations for quantum symmetric pair coideals of Kac-Moody type,” JOURNAL OF COMBINATORIAL ALGEBRA, vol. 5, no. 4, pp. 297–367, 2021.
@article{01GR1H382FTRH8ZVCJGNECZ70M,
  abstract     = {{Classical symmetric pairs consist of a symmetrizable Kac-Moody algebra g, together with its subalgebra of fixed points under an involutive automorphism of the second kind. Quantum group analogs of this construction, known as quantum symmetric pairs, replace the fixed point Lie subalgebras by one-sided coideal subalgebras of the quantized enveloping algebra U_q(g). We provide a complete presentation by generators and relations for these quantum symmetric pair coideal subalgebras. These relations are of inhomogeneous q-Serre type and are valid without restrictions on the generalized Cartan matrix. We draw special attention to the split case, where the quantum symmetric pair coideal subalgebras are generalized q-Onsager algebras.}},
  author       = {{De Clercq, Hadewijch}},
  issn         = {{2415-6302}},
  journal      = {{JOURNAL OF COMBINATORIAL ALGEBRA}},
  keywords     = {{Quantum groups,Kac-Moody algebras,quantum symmetric pairs,coideal subalgebras,q-Onsager algebra,Serre presentation,Dolan-Grady relations}},
  language     = {{eng}},
  number       = {{4}},
  pages        = {{297--367}},
  title        = {{Defining relations for quantum symmetric pair coideals of Kac-Moody type}},
  url          = {{http://doi.org/10.4171/JCA/57}},
  volume       = {{5}},
  year         = {{2021}},
}
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