TBA
Francesca Fedele
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Associative algebras: on polynomial identities and beyond
Ginevra Giordani
In this talk we will introduce the theory of polynomial identities (PI-theory) for associative algebras. After stating the main classical results of PI-theory, we will talk about the main algebraic structures studied from the PI point of view. Finally, we will introduce their generalizations and we will close the talk by presenting research advances.
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Marianne Johnson
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Noncommutative Stone dualities
The talk will present an introduction to the noncommutative duality theory that extends the classical Stone duality between generalized Boolean algebras and locally compact Stone spaces. In these dualities, generalized Boolean algebras are replaced by Boolean inverse, restriction or range semigroups, while locally compact Stone spaces are replaced by ample groupoids or categories. The latter are \'etale groupoids or categories whose unit space is a locally compact Stone space. I will discuss the dualities developed over the last 20 years by Lawson, Resende, Cockett and Garner, and the presenter.
Irreducible representation of free algebras
Francesca Mantese
We present a complete classification of finite dimensional irreducible representations of the free algebra K⟨x₁, ..., xₙ⟩ in terms of irreducible polynomials in the non-commutative variables x₁, ..., xₙ. The main tool is the study of simple modules over the Leavitt algebra Lₖ(1, n), which arises as universal localization of K⟨x₁, ..., xₙ⟩. This approach leads to new insights in the study of the factorization of polynomials in non-commutative variables and other related topics, such as an algorithm to divide polynomials or to compute the greatest common divisor between them. This is part of a joint project with P. N. Anh.
TBA
Nikola Bogdanovic
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