Abstract
We construct a theory that describes a quantum (non-commutative) analogue of representations within the framework of “non-commutative linear geometry” set out in the work of Manin [Quantum groups and noncommutative geometry, Univ. Montréal, Centre de Recherches Mathématiques, Montréal, QC, 1988]. For this purpose, the concept of an internal hom \hom -functor is generalized to the case of parameterized adjunctions, and we construct a general approach to representations of monoids for a symmetric monoidal category with a parameter subcategory. A quantum theory of representations is then obtained by applying this approach to the monoidal category of a certain class of graded algebras with the Manin product, where the parameterizing subcategory consists of connected finitely generated quadratic algebras. We formulate this theory in the language of Manin matrices. We also obtain quantum analogues of the direct sum and tensor product of representations. Finally, we give some examples of quantum representations.
Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callSimilar Papers
Disclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
