Search results for "REPRESENTATION"

A remark on conjectures in modular representation theory

1987

Degrees of Characters and Values on Prime Order Elements

2008

Two irreducible characters of a finite group with the same value on prime elements have the same degree.

On the representation theory of quantum Heisenberg group and algebra

1994

We show that the quantum Heisenberg groupH q (1) and its *-Hopf algebra structure can be obtained by means of contraction from quantumSU q (2) group. Its dual Hopf algebra is the quantum Heisenberg algebraU q (h(1)). We derive left and right regular representations forU q (h(1)) as acting on its dualH q (1). Imposing conditions on the right representation, the left representation is reduced to an irreducible holomorphic representation with an associated quantum coherent state. Realized in the Bargmann-Hilbert space of analytic functions the unitarity of regular representation is also shown. By duality, left and right regular representations for quantum Heisenberg group with the quantum Heis…

Applied Linear Algebra: Electrical Networks

2016

This chapter shows how mathematical theory is not an abstract subject which has no connection with the real world. On the contrary, this entire book is written by stating that mathematics in general, and algebra in this case, is an integrating part of every day real life and that the professional life of computational scientists and engineers requires a solid mathematical background. In order to show how the contents of the previous chapters have an immediate technical application, the last chapter of this book describes a core engineering subject, i.e. electrical networks, as an algebraic exercise. Furthermore, this chapter shows how the combination of the algebraic topics give a natural r…

Koordinatisierung von verallgemeinerten affinen Räumen

1997

Derivations of quasi *-algebras

2004

The spatiality of derivations of quasi*-algebras is investigated by means of representation theory. Moreover, in view of physical applications, the spatiality of the limit of a family of spatial derivations is considered.

Initial Data for Non-Linear Evolution Equations and Differentiable Vectors of Group Representations

1995

Regularity properties of non-linear Lie algebra representations are defined. These properties are satisfied in examples given by evolution equations. We prove that this regularity implies that the set of C ∞ vectors for the non-linear group representation obtained by integration of the Lie algebra representation coincide with the set of C ∞ vectors of the linear part (the order one term) of this group representation.

Characters and Blocks of Finite Groups

1998

This is a clear, accessible and up-to-date exposition of modular representation theory of finite groups from a character-theoretic viewpoint. After a short review of the necessary background material, the early chapters introduce Brauer characters and blocks and develop their basic properties. The next three chapters study and prove Brauer's first, second and third main theorems in turn. These results are then applied to prove a major application of finite groups, the Glauberman Z*-theorem. Later chapters examine Brauer characters in more detail. The relationship between blocks and normal subgroups is also explored and the modular characters and blocks in p-solvable groups are discussed. Fi…

Large orbits ofp-groups on characters and applications to character degrees

2005

We prove that if ap-groupA acts on a solvablep′-groupG then there is a “large” orbit on the ordinary complex irreducible characters ofG. As a consequence of this theorem we obtain results that relate ordinary and Brauer character degrees.

Banach elements and spectrum in Banach quasi *-algebras

2006

A normal Banach quasi -algebra (X;A_0) has a distinguished Banach - algebra X_b consisting of bounded elements of X. The latter -algebra is shown to coincide with the set of elements of X having fi nite spectral radius. If the family P(X) of bounded invariant positive sesquilinear forms on X contains suffi ciently many elements then the Banach -algebra of bounded elements can be characterized via a C -seminorm defi ned by the elements of P(X).