Now showing items 1-20 of 23

• #### Groups with Spanier-Whitehead Duality ﻿

[OWP-2019-23] (Mathematisches Forschungsinstitut Oberwolfach, 2019-09-17)
We introduce the notion of Spanier-Whitehead $K$-duality for a discrete group $G$, defined as duality in the KK-category between two $C*$-algebras which are naturally attached to the group, namely the reduced group ...
• #### Group-Graded Rings Satisfying the Strong Rank Condition ﻿

[OWP-2019-22] (Mathematisches Forschungsinstitut Oberwolfach, 2019-08-16)
A ring $R$ satisfies the $\textit{strong rank condition}$ (SRC) if, for every natural number $n$, the free $R$-submodules of $R^n$ all have rank $\leq n$. Let $G$ be a group and $R$ a ring strongly graded by $G$ such that ...
• #### A Cheeger Type Inequality in Finite Cayley Sum Graphs ﻿

[OWP-2019-21] (Mathematisches Forschungsinstitut Oberwolfach, 2019-07-31) - (5 May - 27 July 2019)
Let $G$ be a finite group and $S$ be a symmetric generating set of $G$ with $|S| = d$. We show that if the undirected Cayley sum graph $C_{\Sigma}(G,S)$ is an expander graph and is non-bipartite, then the spectrum of its ...
• #### On a Cheeger Type Inequality in Cayley Graphs of Finite Groups ﻿

[OWP-2019-20] (Mathematisches Forschungsinstitut Oberwolfach, 2019-07-22) - (7 July - 7 October 2017)
Let $G$ be a finite group. It was remarked by Breuillard-Green-Guralnick-Tao that if the Cayley graph $C(G,S)$ is an expander graph and is non-bipartite then the spectrum of the adjacency operator $T$ is bounded away from ...
• #### On Co-Minimal Pairs in Abelian Groups ﻿

[OWP-2019-19] (Mathematisches Forschungsinstitut Oberwolfach, 2019-07-09)
A pair of non-empty subsets $(W,W')$ in an abelian group $G$ is a complement pair if $W+W'=G$. $W'$ is said to be minimal to $W$ if $W+(W'\setminus \{w'\}) \neq G, \forall \,w'\in W'$. In general, given an arbitrary subset ...
• #### A Quantitative Analysis of the “Lion-Man” Game ﻿

[OWP-2019-18] (Mathematisches Forschungsinstitut Oberwolfach, 2019-07-08)
In this paper we analyze, based on an interplay between ideas and techniques from logic and geometric analysis, a pursuit-evasion game. More precisely, we focus on a discrete lion and man game with an $\varepsilon$-capture ...
• #### On Residuals of Finite Groups ﻿

[OWP-2019-17] (Mathematisches Forschungsinstitut Oberwolfach, 2019-05-28)
A theorem of Dolfi, Herzog, Kaplan, and Lev [DHKL07, Thm. C] asserts that in a finite group with trivial Fitting subgroup, the size of the soluble residual of the group is bounded from below by a certain power of the group ...
• #### Congruences Associated with Families of Nilpotent Subgroups and a Theorem of Hirsch ﻿

[OWP-2019-16] (Mathematisches Forschungsinstitut Oberwolfach, 2019-05-27)
Our main result associates a family of congruences with each suitable system of nilpotent subgroups of a finite group. Using this result, we complete and correct the proof of a theorem of Hirsch concerning the class number ...
• #### Experimenting with Symplectic Hypergeometric Monodromy Groups ﻿

[OWP-2019-15] (Mathematisches Forschungsinstitut Oberwolfach, 2019-05-22)
We present new computational results for symplectic monodromy groups of hypergeometric differential equations. In particular, we compute the arithmetic closure of each group, sometimes justifying arithmeticity. The results ...
• #### Chirality of Real Non-Singular Cubic Fourfolds and Their Pure Deformation Classification ﻿

[OWP-2019-14] (Mathematisches Forschungsinstitut Oberwolfach, 2019-05-15)
In our previous works we have classified real non-singular cubic hypersurfaces in the 5-dimensional projective space up to equivalence that includes both real projective transformations and continuous variations of ...
• #### The Becker-Gottlieb Transfer: a Geometric Description ﻿

[OWP-2019-13] (Mathematisches Forschungsinstitut Oberwolfach, 2019-05-14)
In this note, we examine geometric aspects of the Becker-Gottlieb transfer in terms of the Umkehr and index maps, and rework some classic index theorems, using the cohomological formulae of the Becker-Gottlieb transfer. ...
• #### The Fourier Transform on Harmonic Manifolds of Purely Exponential Volume Growth ﻿

[OWP-2019-12] (Mathematisches Forschungsinstitut Oberwolfach, 2019-05-08)
Let $X$ be a complete, simply connected harmonic manifold of purely exponential volume growth. This class contains all non-flat harmonic manifolds of non-positive curvature and, in particular all known examples of harmonic ...
• #### Minimal Codimension One Foliation of a Symmetric Space by Damek-Ricci Spaces ﻿

[OWP-2019-11] (Mathematisches Forschungsinstitut Oberwolfach, 2019-05-07)
In this article we consider solvable hypersurfaces of the form $N \exp(\mathbb{R} H)$ with induced metrics in the symmetric space $M = SL(3,\mathbb{C})/SU(3)$, where $H$ a suitable unit length vector in the subgroup $A$ ...
• #### On the Lie Algebra Structure of $HH^1(A)$ of a Finite-Dimensional Algebra A ﻿

[OWP-2019-10] (Mathematisches Forschungsinstitut Oberwolfach, 2019-04-17)
Let $A$ be a split finite-dimensional associative unital algebra over a field. The first main result of this note shows that if the Ext-quiver of $A$ is a simple directed graph, then $HH^1(A)$ is a solvable Lie algebra. ...
• #### The First Hochschild Cohomology as a Lie Algebra ﻿

[OWP-2019-09] (Mathematisches Forschungsinstitut Oberwolfach, 2019-04-16)
In this paper we study sufficient conditions for the solvability of the first Hochschild cohomology of a finite dimensional algebra as a Lie algebra in terms of its Ext-quiver in arbitrary characteristic. In particular, ...
• #### On a Group Functor Describing Invariants of Algebraic Surfaces ﻿

[OWP-2019-08] (Mathematisches Forschungsinstitut Oberwolfach, 2019-03-01)
Liedtke (2008) has introduced group functors $K$ and $\tilde K$, which are used in the context of describing certain invariants for complex algebraic surfaces. He proved that these functors are connected to the theory of ...
• #### Weighted Surface Algebras: General Version ﻿

[OWP-2019-07] (Mathematisches Forschungsinstitut Oberwolfach, 2019-02-28)
We introduce general weighted surface algebras of triangulated surfaces with arbitrarily oriented triangles and describe their basic properties. In particular, we prove that all these algebras, except the singular disc, ...
• #### Group Algebras of Compact Groups. A New Way of Producing Group Hopf Algebras over Real and Complex Fields: Weakly Complete Topological Vector Spaces ﻿

[OWP-2019-06] (Mathematisches Forschungsinstitut Oberwolfach, 2019-02-27)
Weakly complete real or complex associative algebras $A$ are necessarily projective limits of finite dimensional algebras. Their group of units $A^{-1}$ is a pro-Lie group with the associated topological Lie algebra \$A_{\rm ...
• #### Hölder Continuity of the Spectra for Aperiodic Hamiltonians ﻿

[OWP-2019-05] (Mathematisches Forschungsinstitut Oberwolfach, 2019-02-26)
We study the spectral location of a strongly pattern equivariant Hamiltonians arising through configurations on a colored lattice. Roughly speaking, two configurations are "close to each other" if, up to a translation, ...
• #### Applications of BV Type Spaces ﻿

[OWP-2019-04] (Mathematisches Forschungsinstitut Oberwolfach, 2019-02-13)