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The purpose of this paper is to put together a large amount of results on the $K (π, 1)$ conjecture for Artin groups, and to make them accessible to non-experts. Firstly, this is a survey, containing basic definitions, the main results, examples and an historical overview of the subject. But, it is also a reference text on the topic that contains proofs of a large part of the results on this question. Some proofs as well as few results are new. Furthermore, the text, being addressed to non-experts, is as...

K2 of p-Adic Group Rings of Abelian p-Groups.

Robert Oliver (1987)

Mathematische Zeitschrift

K3 surfaces with a symplectic automorphism of order 11

Igor Dolgachev, JongHae Keum (2009)

Journal of the European Mathematical Society

Kac-Moody groups, hovels and Littelmann paths

Stéphane Gaussent, Guy Rousseau (2008)

Annales de l’institut Fourier

We give the definition of a kind of building $ℐ$ for a symmetrizable Kac-Moody group over a field $K$ endowed with a discrete valuation and with a residue field containing $ℂ$ . Due to the lack of some important property of buildings, we call it a hovel. Nevertheless, some good ones remain, for example, the existence of retractions with center a sector-germ. This enables us to generalize many results proved in the semisimple case by S. Gaussent and P. Littelmann. In particular, if $K = ℂ ((t))$ , the geodesic segments...

Kappa-Slender Modules

Radoslav Dimitric (2020)

Communications in Mathematics

For an arbitrary infinite cardinal $κ$ , we define classes of $κ$ -cslender and $κ$ -tslender modules as well as related classes of $κ$ -hmodules and initiate a study of these classes.

Kartesisch und residuell abgeschlossene Gruppenklassen [Book]

R. Göbel (1969)

Kazhdan constants for SL (3, Z).

M. Burger (1991)

Journal für die reine und angewandte Mathematik

Kazhdan–Lusztig basis and a geometric filtration of an affine Hecke algebra, II

Nanhua Xi (2011)

Journal of the European Mathematical Society

An affine Hecke algebras can be realized as an equivariant $K$ -group of the corresponding Steinberg variety. This gives rise naturally to some two-sided ideals of the affine Hecke algebra by means of the closures of nilpotent orbits of the corresponding Lie algebra. In this paper we will show that the two-sided ideals are in fact the two-sided ideals of the affine Hecke algebra defined through two-sided cells of the corresponding affine Weyl group after the two-sided ideals are tensored by $ℚ$ . This...

Kazhdan-Lusztig polynomials: history, problems, and combinatorial invariance.

Brenti, Francesco (2002)

Séminaire Lotharingien de Combinatoire [electronic only]

k-counting automata

Joël Allred, Ulrich Ultes-Nitsche (2012)

RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications

In this paper, we define k-counting automata as recognizers for ω-languages, i.e. languages of infinite words. We prove that the class of ω-languages they recognize is a proper extension of the ω-regular languages. In addition we prove that languages recognized by k-counting automata are closed under Boolean operations. It remains an open problem whether or not emptiness is decidable for k-counting automata. However, we conjecture strongly that it is decidable and give formal reasons why we believe...

k-counting automata

Joël Allred, Ulrich Ultes-Nitsche (2012)

RAIRO - Theoretical Informatics and Applications

k-Homogeneous Groups.

William M. Kantor (1972)

Mathematische Zeitschrift

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