<div dir="ltr"><font style="font-family:arial,sans-serif" size="4">Değerli liste üyeleri,</font><font style="font-family:arial,sans-serif" size="4"><br>MSGSÜ Matematik Bölümü Genel Seminerleri'nde bu hafta konuşmacımız Oklahoma Üniversitesi Matematik Bölümü'nden <span>Murad Özaydın</span>. </font><font style="font-family:arial,sans-serif" size="4"><br><br>Konuşma özeti ektedir</font><font style="font-family:arial,sans-serif" size="4">.</font><font style="font-family:arial,sans-serif" size="4"><br>Seminerde görüşmek üzere,</font><font style="font-family:arial,sans-serif" size="4"><br>Selamlar,</font><font style="font-family:arial,sans-serif" size="4"><br><br>Kıvanç Ersoy</font><font size="4"><b><font size="6"><br><br><br>-----------------------------------------<br><br><br>MSGSÜ Mathematics Seminar</font></b></font><div style="text-align:center"><font size="4"><br><font size="6">Murad Özaydın</font></font></div><div class="gmail_extra"><div class="gmail_quote"><div dir="ltr"> <b><font size="4"><font size="4"><br><br></font></font></b><div style="text-align:center"><font size="6"><b>Leavitt Path Algebras</b></font><br></div><font size="4"><font size="4"><br>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 <span>Leavitt</span>
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 <span>Leavitt</span> (1962) and their analytic cousins the C*-<span>algebras</span>
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 <span>algebras</span> generated by the downsampling and upsampling operators). Moreover <span>Leavitt</span>'s
work (1962, 1965) provided important impetus for major developments in
non- commutative ring theory in the 1970s by Cohn, Bergman and others. <br><br>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)<span></span><span></span>. LPAs are (Cohn) localizations of Path (or Quiver) <span>Algebras</span>
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.</font></font><div class=""><div id=":2dr" class="" tabindex="0"><img class="" src="https://ssl.gstatic.com/ui/v1/icons/mail/images/cleardot.gif"></div></div><font size="4"><font size="4"><br>MSGSÜ, Bomonti Kampüsü, <br><br>Matematik Bölümü Seminer <span style="background-color:rgb(255,255,204)"></span>Odası.<br></font></font></div><div dir="ltr"> <font size="4"><font size="4"><br>03.03.2016, Perşembe, 16:00</font></font></div></div><br></div></div>