[Turkmath:7368] Feza Gürsey Fizik ve Matematik UygAr Merkezi::Genel Seminer

[kazimilhan.ikeda]

Değerli Matematikçiler,

23 Ocak 2026 Cuma günü saat 13:30'da Feza Gürsey Fizik ve Matematik 
UygAr Merkezi Genel Seminerleri kapsamında yüz yüze yapılacak olan 
konuşma detayları aşağıdadır.

İyi çalışmalar,
İlhan İkeda

"Leibniz prop is a crossed presimplicial algebra"

Murat Can Aşkaroğulları (Gebze Teknik Üniversitesi)

Abstract:
Leibniz algebras, introduced by Loday and Pirashvili, are analogues of 
Lie algebras that are not skew-symmetric. Just as in the Lie case, 
Leibniz algebras are governed by an operad and can be modeled by an 
associated PROP. We prove that the Leibniz PROP is isomorphic as k
-linear categories (not as monoidal categories) to the symmetric crossed 
presimplicial algebra k[(Δ+)opS] where Δ+ is the presimplicial category, 
but the distributive law between (Δ+)op and the symmetric groups 
S=⨆n≥1Sn is not the standard one. In establishing this result, we also 
extend the standard distributive law between k[(Δ+)op] and k[S] to a 
distributive law between the nonsymmetric magmatic PROP and Artin's 
braid monoid k[B] where B=⨆n≥1Bn. Furthermore, our proof yields a 
description of the boundary maps on the Loday complex as alternating 
sums of partial boundary maps. This is a joint work with Atabey Kaygun.

NOT: Seminer konuşması FGE-Merkez Bina'da yapılacaktır.
Ulaşım: https://fezagursey.bogazici.edu.tr/tr/ulasim