Manin matrices for quadratic algebras. (English) Zbl 1491.16036
Summary: We give a general definition of Manin matrices for arbitrary quadratic algebras in terms of idempotents. We establish their main properties and give their interpretation in terms of the category theory. The notion of minors is generalised for a general Manin matrix. We give some examples of Manin matrices, their relations with Lax operators and obtain the formulae for some minors. In particular, we consider Manin matrices of the types \(B, C\) and \(D\) introduced by A. Molev [Sugawara operators for classical Lie algebras. Providence, RI: American Mathematical Society (AMS) (2018; Zbl 1395.17001)] and their relation with Brauer algebras. Infinite-dimensional Manin matrices and their connection with Lax operators are also considered.
MSC:
| 16T99 | Hopf algebras, quantum groups and related topics |
| 17B37 | Quantum groups (quantized enveloping algebras) and related deformations |
| 81R50 | Quantum groups and related algebraic methods applied to problems in quantum theory |
Citations:
Zbl 1395.17001References:
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