KGTA seminar, 19. septembar 2017.

Naredni sastanak Seminara biće održan u utorak, 19. septembra 2017, u sali 844 Matematičkog fakulteta sa početkom u 14 časova.

Predavač: Leon Lampret, Faculty of computer and information science, Ljubljana, Slovenia

Naslov predavanja: TORSION TABLE FOR THE LIE ALGEBRA niln

Apstrakt: 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 pm-torsion appears in H*(niln;Z) for pm-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}.

Napomena: Predavanje na interesantan način povezuje (ko)homologiju, Liove algebre i enumerativnu kombinatoriku. Predavanje je namenjeno širem krugu slušalaca i svi osnovni pojmovi će biti uvedeni na predavanju.



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