Noncommutative Algebras, Their Applications and Generalizations
A special issue of Mathematics (ISSN 2227-7390). This special issue belongs to the section "Computational and Applied Mathematics".
Deadline for manuscript submissions: closed (29 February 2020) | Viewed by 589
Special Issue Editor
2. Department of Mathematics, University of Białystok, K. Ciołkowskiego 1M, 15-245 Białystok, Poland
Interests: noncommutative geometry; corings and comodules; Hopf algebras; category theory; algebraic structures
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Special Issue Information
Dear Colleagues,
Associative algebras are one of the most fundamental and prevalent structures in modern mathematics, whether of pure or applied flavor. Their applications range from geometry through topology and analysis to physics. Traditionally commutative algebras are associated with geometry (e.g., as coordinate algebras of algebraic varieties or smooth functions on manifolds) and with classical physics (e.g., as algebras of observables in classical mechanics). Noncommutative algebras can be linked to quantum physics (e.g., as operator algebras of observables in quantum mechanics). Combining the geometric and quantum mechanical links with algebras, one can view noncommutative algebras as encoding functions on objects in noncommutative geometry.
I would like to invite contributions to this special volume which explore new developments of noncommutative algebras and related structures (such as Hopf algebras, coalgebras, or corings), in particular with their geometric meaning in mind, together with their applications to other fields. Since algebraic geometry relies heavily on categorical constructions, articles which explore connections between noncommutative algebras and category theory are most welcome. Finally, various applications of noncommutative algebras might lead to the necessity of widening the perspective and thus force one to go beyond traditional associative algebras, for example, in the direction of universal algebra considerations. Contributions leaning towards this direction are welcome, too.
Prof. Dr. Tomasz Brzezinski
Guest Editor
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Keywords
- associative algebra
- noncommutative algebras
- noncommutative geometry
- algebras with additional structure (Hopf algebras, operator algebras)
- applications of algebras in mathematics and physics
