## 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

### Keywords:

chains of twists; primitivization of subalgebras
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