GRAPH ALGEBRAS RELATED TO CREATORS ON FOCK SPACES

Speaker(s)

ANNA WYSOCZAŃSKA-KULA

Affiliation

Uniwersytet Wrocławski, Poland

Language of the talk

English

Date

Oct. 21, 2026, 5:15 p.m.

Title in Polish

GRAPH ALGEBRAS RELATED TO CREATORS ON FOCK SPACES

Seminar

North Atlantic Noncommutative Geometry Seminar

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Developed by V. A. Fock in 1932, Fock spaces (bosonic and fermionic) are mathematical structures that model quantum systems containing a variable or unspecified number of identical particles. They come naturally equipped with creation and annihilation operators, and the properties of C*-algebras generated by these creation operators have been studied extensively. With the introduction of different non-commutative independences (the free independence at the forefront), more Fock-type spaces emerged, each one with its own creation and annihilation operators, as well as C*-algebras generated by them. Surprisingly often, it turned out  that they are closely related to graph algebras. First, D. Evans observed  in 1980 the relation between the algebras of creators on the free Fock spaces and the Cuntz algebras. More recently, Griseta and Wysoczański showed in 2025 that a finite number of monotone creators generate a quotient of a certain graph algebra. Also, Crismale, Vecchio, Rossi, and Wysoczański proved that the algebras of infinitely many creators on the (weakly) monotone Fock spaces are *-isomorphic to Exel-Laca algebras or their quotients. During the talk, I will discuss a generalization of the latter results concerning the algebra of infinitely many creators on the boolean-anti-monotone Fock space. For the index set having a tree-like structure, I will link it to Exel-Laca algebras and further to graph algebras. This enables one to deduce many of the properties of the algebras in question. Based on joint work with Jack Spielberg and Janusz Wysoczański.

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