scholarly journals Hecke algebras from groups acting on trees and HNN extensions

2009 ◽  
Vol 321 (11) ◽  
pp. 3065-3088 ◽  
Author(s):  
Udo Baumgartner ◽  
Marcelo Laca ◽  
Jacqui Ramagge ◽  
George Willis
Keyword(s):  
Hecke Algebras ◽  
Hnn Extensions ◽  
Groups Acting On Trees

scholarly journals C*-SIMPLE GROUPS: AMALGAMATED FREE PRODUCTS, HNN EXTENSIONS, AND FUNDAMENTAL GROUPS OF 3-MANIFOLDS

2011 ◽  
Vol 03 (04) ◽  
pp. 451-489 ◽  
Author(s):  
PIERRE DE LA HARPE ◽  
JEAN-PHILIPPE PRÉAUX
Keyword(s):  
Sufficient Conditions ◽  
Simple Groups ◽  
Fundamental Groups ◽  
Normal Subgroups ◽  
Free Products ◽  
Amalgamated Free Products ◽  
Hnn Extensions ◽  
Groups Acting On Trees ◽  
Jsj Decompositions ◽  
Fixed Point Sets

We establish sufficient conditions for the C*-simplicity of two classes of groups. The first class is that of groups acting on trees, such as amalgamated free products, HNN-extensions, and their nontrivial subnormal subgroups; for example normal subgroups of Baumslag–Solitar groups. The second class is that of fundamental groups of compact 3-manifolds, related to the first class by their Kneser–Milnor and JSJ decompositions. Much of our analysis deals with conditions on an action of a group Γ on a tree T which imply the following three properties: abundance of hyperbolic elements, better called strong hyperbolicity, minimality, both on the tree T and on its boundary ∂T, and faithfulness in a strong sense. An important step in this analysis is to identify automorphisms of T which are slender, namely such that their fixed-point sets in ∂T are nowhere dense for the shadow topology.

scholarly journals C * -simplicity of HNN extensions and groups acting on trees

2021 ◽  
Vol 70 (4) ◽  
pp. 1497-1543
Author(s):  
Rasmus Sylvester Bryder ◽  
Nikolay A. Ivanov ◽  
Tron Omland
Keyword(s):  
Hnn Extensions ◽  
Groups Acting On Trees

scholarly journals Dominant and global dimension of blocks of quantised Schur algebras

2021 ◽  
Author(s):  
Ming Fang ◽  
Wei Hu ◽  
Steffen Koenig
Keyword(s):  
Hecke Algebras ◽  
Symmetric Groups ◽  
Global Dimension ◽  
Group Algebras ◽  
Dominant Dimension ◽  
Schur Algebras ◽  
Homological Dimensions ◽  
Weyl Duality

AbstractGroup algebras of symmetric groups and their Hecke algebras are in Schur-Weyl duality with classical and quantised Schur algebras, respectively. Two homological dimensions, the dominant dimension and the global dimension, of the indecomposable summands (blocks) of these Schur algebras S(n, r) and $$S_q(n,r)$$ S q ( n , r ) with $$n \geqslant r$$ n ⩾ r are determined explicitly, using a result on derived invariance in Fang, Hu and Koenig (J Reine Angew Math 770:59–85, 2021).

scholarly journals The residual finiteness of HNN-extensions and generalized free products of nilpotent groups: a characterization

1992 ◽  
Vol 53 (3) ◽  
pp. 408-420 ◽  
Author(s):  
E. Raptis ◽  
D. Varsos
Keyword(s):  
Nilpotent Groups ◽  
Residual Finiteness ◽  
Finitely Generated ◽  
Free Products ◽  
Hnn Extensions ◽  
Base Group ◽  
Generalized Free Products

AbstractWe study the residual finiteness of free products with amalgamations and HNN-extensions of finitely generated nilpotent groups. We give a characterization in terms of certain conditions satisfied by the associated subgroups. In particular the residual finiteness of these groups implies the possibility of extending the isomorphism of the associated subgroups to an isomorphism of their isolated closures in suitable overgroups of the factors (or the base group in case of HNN-extensions).

scholarly journals Laurent phenomenon and simple modules of quiver Hecke algebras

2019 ◽  
Vol 155 (12) ◽  
pp. 2263-2295 ◽  
Author(s):  
Masaki Kashiwara ◽  
Myungho Kim
Keyword(s):  
Simple Module ◽  
Hecke Algebras ◽  
Duke Math ◽  
Cluster Algebras ◽  
Coordinate Ring ◽  
Simple Modules ◽  
Laurent Phenomenon ◽  
Cluster Variable ◽  
Quantum Cluster

In this paper we study consequences of the results of Kang et al. [Monoidal categorification of cluster algebras, J. Amer. Math. Soc. 31 (2018), 349–426] on a monoidal categorification of the unipotent quantum coordinate ring $A_{q}(\mathfrak{n}(w))$ together with the Laurent phenomenon of cluster algebras. We show that if a simple module $S$ in the category ${\mathcal{C}}_{w}$ strongly commutes with all the cluster variables in a cluster $[\mathscr{C}]$, then $[S]$ is a cluster monomial in $[\mathscr{C}]$. If $S$ strongly commutes with cluster variables except for exactly one cluster variable $[M_{k}]$, then $[S]$ is either a cluster monomial in $[\mathscr{C}]$ or a cluster monomial in $\unicode[STIX]{x1D707}_{k}([\mathscr{C}])$. We give a new proof of the fact that the upper global basis is a common triangular basis (in the sense of Qin [Triangular bases in quantum cluster algebras and monoidal categorification conjectures, Duke Math. 166 (2017), 2337–2442]) of the localization $\widetilde{A}_{q}(\mathfrak{n}(w))$ of $A_{q}(\mathfrak{n}(w))$ at the frozen variables. A characterization on the commutativity of a simple module $S$ with cluster variables in a cluster $[\mathscr{C}]$ is given in terms of the denominator vector of $[S]$ with respect to the cluster $[\mathscr{C}]$.

scholarly journals Rouquier blocks of the cyclotomic Hecke algebras of G(de, e, r)

2010 ◽  
Vol 197 ◽  
pp. 175-212
Author(s):  
Maria Chlouveraki
Keyword(s):  
Infinite Series ◽  
Hecke Algebras ◽  
Weyl Groups ◽  
Reflection Groups ◽  
Complex Reflection ◽  
Complex Reflection Groups ◽  
Cyclotomic Hecke Algebras

The Rouquier blocks of the cyclotomic Hecke algebras, introduced by Rouquier, are a substitute for the families of characters defined by Lusztig for Weyl groups, which can be applied to all complex reflection groups. In this article, we determine them for the cyclotomic Hecke algebras of the groups of the infinite seriesG(de, e, r), thus completing their calculation for all complex reflection groups.

HIGH DIMENSIONAL KNOT GROUPS AND HNN EXTENSIONS OF THE FIBONACCI GROUPS

1998 ◽  
Vol 07 (04) ◽  
pp. 503-508 ◽  
Author(s):  
ANDRZEJ SZCZEPAŃSKI
Keyword(s):  
High Dimensional ◽  
New Class ◽  
Hnn Extensions

We shall present a new class of examples of high dimensional knot groups. All of them are HNN extensions of the Fibonacci groups. We give also some characterization of these groups.

scholarly journals Hecke Algebras and Monoid Conjugacy Classes

1995 ◽  
Vol 173 (3) ◽  
pp. 499-517 ◽  
Author(s):  
M.S. Putcha
Keyword(s):  
Hecke Algebras ◽  
Conjugacy Classes
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