ὅδε οἶκος, ὦ ἑταῖρε, μνημεῖον ἐστιν ζῴων τῶν σοφῶν ἀνδρῶν, καὶ τῶν ἔργων αὐτῶν

Seminar for Combinatorics, Geometry, Algebra and Topology

 

PROGRAM


Seminar Kombinatorika, Geometrija, Topologija, Algebra (KGTA)

PLAN RADA ZA SEPTEMBAR 2017:



UTORAK, 19.09.2017. od 14:00 - 16:00, Matematički fakultet Beograd, sala 844 (5. sprat)
Leon Lampret, Faculty of computer and information science, Ljubljana, Slovenia
TORSION TABLE FOR THE LIE ALGEBRA niln
We study the Lie ring niln of all strictly upper-triangular n×n matrices with entries in Z. Its complete homology for n≤8 is computed. We prove that every p^m-torsion appears in H∗(niln;Z) for p^m≤n−2. For m=1, Dwyer proved that the bound is sharp, i.e. there is no p-torsion in H∗(niln;Z) when prime p>n−2. In general, for m>1 the bound is not sharp, as we show that there is 8-torsion in H*(nil8;Z). As a sideproduct, we derive the known result, that the ranks of the free part of H*(niln;Z) are the Mahonian numbers (=number of permutations of [n] with k inversions), using a different approach than in [KostantLAHGBWT}.

UTORAK, 26.09.2017. od 14:00 - 16:00, Matematički fakultet Beograd, sala 844 (5. sprat)
Marija Jelić, Đorđe Baralić, Vladimir Grujić, i dr.
MATEMATIKA I PUTOPISI
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