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13 października 2026 / Oct 13, 2026
Anna Wysoczańska-Kula (Wrocław University)
What does graph algebras have to do with creators?
Abstract. Since the introduction of bosonic and fermionic Fock spaces by V.A. Fock in 1932, many different Fock-type constructions emerged. They always come naturally equipped with creation and annihilation operators, and, in some cases, the C*-algebras generated by these families reveal surprising connections to graph algebras. For instance, in 1980, D. Evans observed that the algebras of creators on the free Fock spaces are tightly related to the Cuntz algebras. More recently, Griseta and Wysoczański showed that a finite number of creators on monotone Fock space generate a quotient of a certain graph algebra. In parallel, Crismale, Vecchio, Rossi, and Wysoczański showed that the algebras of infinitely many creators on the monotone Fock spaces is *-isomorphic to Exel-Laca algebras or their quotients. During the talk, I will discuss an extension of these results to the algebra of creators on the boolean-antimonotone Fock space.
This is joint work with Jack Spielberg and Janusz Wysoczański.