[Turkmath:1070] MSGSÜ Matematik Semineri, 3 Mart 2016, Murad Özaydın

[Kıvanç Ersoy]

Değerli liste üyeleri,
MSGSÜ Matematik Bölümü Genel Seminerleri'nde bu hafta konuşmacımız Oklahoma
Üniversitesi Matematik Bölümü'nden Murad Özaydın.

Konuşma özeti ektedir.
Seminerde görüşmek üzere,
Selamlar,

Kıvanç Ersoy





*-----------------------------------------MSGSÜ Mathematics Seminar*

Murad Özaydın


*Leavitt Path Algebras*

LPAs (Leavitt Path Algebras) were defined recently (Abrams and Aranda Pino,
2005; Ara, Moreno and Pardo, 2007) but they have roots in the works of
Leavitt in the 60s focused on understanding the extent of the failure of
the IBN (Invariant Basis Number) property for arbitrary rings. A ring has
IBN if any two bases of a finitely generated free module have the same
number of elements. Fields, division rings, commutative rings, Noetherian
rings all have IBN. However, the rings L(1,n) defined by Leavitt (1962) and
their analytic cousins the C*-algebras of Cuntz (1977) are not artificial
and pathological structures constructed only for the sake of providing
counter examples; for instance, they implicitly come up in Signal
Processing (as the algebras generated by the downsampling and upsampling
operators). Moreover Leavitt's work (1962, 1965) provided important impetus
for major developments in non- commutative ring theory in the 1970s by
Cohn, Bergman and others.

I plan to start with the basic definitions, state some fundamental results,
explain the criterion for an LPA to have IBN (joint work with Muge Kanuni
Er) and indicate the ideas involved in the recent classification of the
finite dimensional representations (jointly with Ayten Koc). LPAs are
(Cohn) localizations of Path (or Quiver) Algebras whose finite dimensional
representations are usually wild, but the category of finite dimensional
representations of LPAs turn out to be tame with a very reasonable
classification of all the indecomposables and the simples. All finite
dimensional quotients of LPAs are also easy to describe.

MSGSÜ, Bomonti Kampüsü,

Matematik Bölümü Seminer Odası.

03.03.2016, Perşembe, 16:00
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