Naslov
Centrally stable algebras

Autori
Gogić, Ilja

Vrsta, podvrsta i kategorija rada
Sažeci sa skupova, sažetak, znanstveni

Skup
2nd Zagreb Workshop on Operator Theory

Mjesto i datum
Zagreb, Hrvatska, 29.06.2020. - 30.06.2020

Vrsta sudjelovanja
Predavanje

Vrsta recenzije
Međunarodna recenzija

Ključne riječi
Centrally stable algebra ; Centrally stable element ; Center ; Radical ; Tensor product of algebras ; Finite-dimensional algebra

Sažetak
Motivated by Vesterstrøm’s characterization of unital weakly central C*-algebras via the centre-quotient property, we introduce the class of centrally stable algebras, as algebras A with the property that for any algebra epimorphism φ:A→B, the centre Z(B) of B is equal to φ(Z(A)), the image of the centre of A. After providing some examples and basic observations, we establish our main result which states that a finite-dimensional unital algebra A over a perfect field F is centrally stable if and only if and only if A\cong (C_1⊗F_1 A_1) × · · · × (C_r ⊗F_r A_r), where each F_i is a finite field extension of F, C_i is a commutative F_i-algebra, and A_i is a central simple F_i-algebra. This is joint work with Matej Brešar (University of Ljubljana and University of Maribor).

Izvorni jezik
Engleski

Znanstvena područja
Matematika

POVEZANOST RADA