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58
result(s) for
"Non-Abelian groups."
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Crossed Products by Hecke Pairs
The author develops a theory of crossed products by actions of Hecke pairs (G, \\Gamma ), motivated by applications in non-abelian C^*-duality. His approach gives back the usual crossed product construction whenever G / \\Gamma is a group and retains many of the aspects of crossed products by groups. The author starts by laying the ^*-algebraic foundations of these crossed products by Hecke pairs and exploring their representation theory and then proceeds to study their different C^*-completions. He establishes that his construction coincides with that of Laca, Larsen and Neshveyev whenever they are both definable and, as an application of his theory, he proves a Stone-von Neumann theorem for Hecke pairs which encompasses the work of an Huef, Kaliszewski and Raeburn.
eBook
The Pinch Technique and its Applications to Non-Abelian Gauge Theories
Non-Abelian gauge theories, such as quantum chromodynamics (QCD) or electroweak theory, are best studied with the aid of Green's functions that are gauge-invariant off-shell, but unlike for the photon in quantum electrodynamics, conventional graphical constructions fail. The Pinch Technique provides a systematic framework for constructing such Green's functions, and has many useful applications. Beginning with elementary one-loop examples, this book goes on to extend the method to all orders, showing that the Pinch Technique is equivalent to calculations in the background field Feynman gauge. The Pinch Technique Schwinger-Dyson equations are derived, and used to show how a dynamical gluon mass arises in QCD. Applications are given to the center vortex picture of confinement, the gauge-invariant treatment of resonant amplitudes, the definition of non-Abelian effective charges, high-temperature effects, and even supersymmetry. This book is ideal for elementary particle theorists and graduate students.
eBook
Computational and experimental group theory : AMS-ASL Joint Special Session, Interactions Between Logic, Group Theory and Computer Science, January 15-16, 2003, Baltimore, Maryland
Since its origin in the early 20th century, combinatorial group theory has been primarily concerned with algorithms for solving particular problems on groups given by generators and relations: word problems, conjugacy problems, isomorphism problems, etc. Recent years have seen the focus of algorithmic group theory shift from the decidability/undecidability type of result to the complexity of algorithms. Papers in this volume reflect that paradigm shift. Articles are based on the AMS/ASL Joint Special Session, Interactions Between Logic, Group Theory and Computer Science. The volume is suitable for graduate students and research mathematicians interested in computational problems of group theory.
eBook
Witten Non Abelian Localization for Equivariant K-Theory, and the 𝑄,𝑅=0 Theorem
The purpose of the present memoir is two-fold. First, we obtain a non-abelian localization theorem when M is any even dimensional
compact manifold : following an idea of E. Witten, we deform an elliptic symbol associated to a Clifford bundle on M with a vector field
associated to a moment map. Second, we use this general approach to reprove the [Q,R] = 0 theorem of Meinrenken-Sjamaar in the
Hamiltonian case, and we obtain mild generalizations to almost complex manifolds. This non-abelian localization theorem can be used to
obtain a geometric description of the multiplicities of the index of general
eBook
Aα matrix of commuting graphs of non-abelian groups
For a finite group G and a subset X≠∅ of G , the commuting graph, indicated by G=C(G,X) , is the simple connected graph with vertex set X and two distinct vertices x and y are edge connected in G if and only if they commute in X . The Aα matrix of G is specified as Aα(G)=αD(G)+(1−α)A(G),α∈[0,1] , where D(G) is the diagonal matrix of vertex degrees while A(G) is the adjacency matrix of G. In this article, we investigate the Aα matrix for commuting graphs of finite groups and we also find the Aα eigenvalues of the dihedral, the semidihedral and the dicyclic groups. We determine the upper bounds for the largest Aα eigenvalue for these graphs. Consequently, we get the adjacency eigenvalues, the Laplacian eigenvalues, and the signless Laplacian eigenvalues of these graphs for particular values of α. Further, we show that these graphs are Laplacian integral.
Journal Article
SCHUR’S COLOURING THEOREM FOR NONCOMMUTING PAIRS
For
$G$
a finite non-Abelian group we write
$c(G)$
for the probability that two randomly chosen elements commute and
$k(G)$
for the largest integer such that any
$k(G)$
-colouring of
$G$
is guaranteed to contain a monochromatic quadruple
$(x,y,xy,yx)$
with
$xy\\neq yx$
. We show that
$c(G)\\rightarrow 0$
if and only if
$k(G)\\rightarrow \\infty$
.
Journal Article
Real Non-Abelian Mixed Hodge Structures for Quasi-Projective Varieties: Formality and Splitting
We define and construct mixed Hodge structures on real schematic homotopy types of complex quasi-projective varieties, giving mixed
Hodge structures on their homotopy groups and pro-algebraic fundamental groups. We also show that these split on tensoring with the ring
eBook
Classification of p-groups via their 2-nilpotent multipliers
For a p-group of order pn, it is known that the order of 2-nilpotent multiplier is equal to ∣M(2)(G)∣=p21n(n−1)(n−2)+3−s2(G), for an integer s2(G). In this article, we characterize all non-abelian p-groups satisfying s2(G)∈{1,2,3}.
Journal Article