Noncommutative Boundaries for Tensor Algebras (20frg248)


Marcelo Laca (University of Victoria)

(University of Illinois UC)

(Newcastle University)


The Banff International Research Station will host the "Noncommutative Boundaries for Tensor Algebras" workshop in Banff from March 1, 2020 to March 8, 2020.

Algebras of operators on Hilbert space are the mathematical models of quantum mechanical systems. The algebra associated to a quantum system is naturally selfadjoint, in the sense that if it contains an operator it also contain its adjoint. The observables are encoded by operators that are equal to their adjoints and the probability of observing a certain range of values is determined by a state, which is a positive linear functional. The motivation to consider a nonselfadjoint tensor algebra is that certain distinguished operators, such as the so-called creation operators that signal the creation of a new particle in a system, are essentially different from their adjoints, the annihilation operators that eliminate the particle. The present project aims to elucidate the relation between a large class of tensor algebras generated by creation operators and the associated selfadjoint algebras that contains both the creation operators and the associated annihilation operators in a canonical minimal way.

The Banff International Research Station for Mathematical Innovation and Discovery (BIRS) is a collaborative Canada-US-Mexico venture that provides an environment for creative interaction as well as the exchange of ideas, knowledge, and methods within the Mathematical Sciences, with related disciplines and with industry. The research station is located at The Banff Centre in Alberta and is supported by Canada's Natural Science and Engineering Research Council (NSERC), the U.S. National Science Foundation (NSF), Alberta's Advanced Education and Technology, and Mexico's Consejo Nacional de Ciencia y Tecnología (CONACYT).