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Displaying 101 – 120 of 140

Self-equivalences of the derived category of Brauer tree algebras with exceptional vertex.

Zimmermann, Alexander (2001)

Analele Ştiinţifice ale Universităţii “Ovidius" Constanţa. Seria: Matematică

Serie de Poincaré-Koszul associée aux groupes de tresses pures.

T. Kohno (1985)

Inventiones mathematicae

Singular Hecke algebras, Markov traces, and HOMFLY-type invariants

Luis Paris, Loïc Rabenda (2008)

Annales de l’institut Fourier

We define the singular Hecke algebra $ℋ (S B_{n})$ as the quotient of the singular braid monoid algebra $ℂ (q) [S B_{n}]$ by the Hecke relations $σ_{k}^{2} = (q - 1) σ_{k} + q$ , $1 \leq k \leq n - 1$ . We define the notion of Markov trace in this context, fixing the number $d$ of singular points, and we prove that a Markov trace determines an invariant on the links with $d$ singular points which satisfies some skein relation. Let ${TR}_{d}$ denote the set of Markov traces with $d$ singular points. This is a $ℂ (q, z)$ -vector space. Our main result is that ${TR}_{d}$ is of dimension $d + 1$ . This result is completed...

Some stability properties of Teichmüller modular function fields with pro-l weight structures.

H. Nakamura, N. Takao, R. Ueno (1995)

Mathematische Annalen

Special positions for surfaces bounded by closed braids.

Lee Rudolph (1985)

Revista Matemática Iberoamericana

Sur les représentations de Krammer génériques

Ivan Marin (2007)

Annales de l’institut Fourier

Nous définissons une représentation des groupes d’Artin de type $A D E$ par monodromie de systèmes KZ généralisés, dont nous montrons qu’elle est isomorphe à la représentation de Krammer généralisée définie originellement par A.M.Cohen et D.Wales, et indépendamment par F.Digne. Cela implique que tous les groupes d’Artin purs de type sphérique sont résiduellement nilpotents-sans-torsion, donc (bi-)ordonnables. En utilisant cette construction nous montrons que ces représentations irréductibles sont Zariski-denses...

The 4-string braid group $B_{4}$ has property RD and exponential mesoscopic rank

Sylvain Barré, Mikaël Pichot (2011)

Bulletin de la Société Mathématique de France

We prove that the braid group $B_{4}$ on 4 strings, its central quotient $B_{4} / 〈 z 〉$ , and the automorphism group $Aut (F_{2})$ of the free group $F_{2}$ on 2 generators, have the property RD of Haagerup–Jolissaint. We also prove that the braid group $B_{4}$ is a group of intermediate mesoscopic rank (of dimension 3). More precisely, we show that the above three groups have exponential mesoscopic rank, i.e., that they contain exponentially many large flat balls which are not included in flats.