Geodesic
Diagonal reduction algebra for~$\mathfrak{osp}(1|2)$
Teoretičeskaâ i matematičeskaâ fizika, Tome 210 (2022) no. 2, pp. 179-198

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The problem of providing complete presentations of reduction algebras associated to a pair of Lie algebras $(\mathfrak{G},\mathfrak{g})$ has previously been considered by Khoroshkin and Ogievetsky in the case of the diagonal reduction algebra for $\mathfrak{gl}(n)$. In this paper, we consider the diagonal reduction algebra of the pair of Lie superalgebras $(\mathfrak{G},\mathfrak{g})$ as a double coset space having an associative $\scriptstyle\lozenge$-product and give a complete presentation in terms of generators and relations. We also provide a PBW basis for this reduction algebra along with Casimir-like elements and a subgroup of automorphisms.
Keywords: reduction algebra, orthosymplectic Lie superalgebra, extremal projector, associative superalgebra.
Mots-clés : Zhelobenko algebra 
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     author = {J. T. Hartwig and D. A. Williams II},
     title = {Diagonal reduction algebra for~$\mathfrak{osp}(1|2)$},
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J. T. Hartwig; D. A. Williams II. Diagonal reduction algebra for~$\mathfrak{osp}(1|2)$. Teoretičeskaâ i matematičeskaâ fizika, Tome 210 (2022) no. 2, pp. 179-198. http://geodesic.mathdoc.fr/item/TMF_2022_210_2_a0/