2012/11/05 by Piotr M. Sołtan, Sołtan, Piotr M.
Mathematics · #20G42 #45L85 #45L89 #Advanced Operator Algebra Research #Advanced Topics in Algebra #Algebraic structures and combinatorial models #FOS: Mathematics #Functional Analysis (math.FA) #Operator Algebras (math.OA)
paper · pdf · doi:10.48550/arxiv.1211.0827
openalex publication_date 2012/11/05 · openalex created_date 2022/10/03 · openalex updated_date 2026/07/28
In this survey article we give basic introduction to the theory of quantum families of maps. We begin with a general look at non-commutative (or "quantum") topology. Then we formulate all our results in this language. Existence of quantum families possessing special properties is discussed and we show that these quantum spaces are canonically endowed with quantum semigroup structures. Classical analogy is emphasized at each step and many examples are described.