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Full chains of twists for orthogonal algebras. (English) Zbl 1050.81563

Summary: We show that for some Hopf subalgebras in \(U_\mathcal F(\text{so}(M))\) nontrivially deformed by a twist \(\mathcal F\) it is possible to find the nonlinear primitive copies. This enlarges the possibilities to construct chains of twists. For orthogonal algebra \(U(\text{so}(M))\) we present a method to compose the full chains with carrier space as large as the Borel subalgebra \(B(\text{so}(M))\). These chains can be used to construct the new deformed Yangians.

MSC:

81R50 Quantum groups and related algebraic methods applied to problems in quantum theory
17B37 Quantum groups (quantized enveloping algebras) and related deformations
81-06 Proceedings, conferences, collections, etc. pertaining to quantum theory
81R15 Operator algebra methods applied to problems in quantum theory
81R25 Spinor and twistor methods applied to problems in quantum theory
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