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On the Loewy structure of the projective indecomposable representations of some stabilizer subgroups of A(8) in characteristic 2
Title
On the Loewy structure of the projective indecomposable representations of some stabilizer subgroups of A(8) in characteristic 2.
Creator
Hindman, Peter Blake, Florida Atlantic University, Klingler, Lee
Abstract/Description
Given a module over a ring for which the Jordan-Holder theorem is valid, the Loewy series is a filtration on the composition factors of the module yielding information on the structure in which they are arranged in the module. We derive subgroups of A8 by considering stabilizers of n-tuples derived from partitions of eight letters, and develop their representation theory over a field of characteristic 2, relying heavily on methods of passing information to groups from their subgroups, with...
Show moreGiven a module over a ring for which the Jordan-Holder theorem is valid, the Loewy series is a filtration on the composition factors of the module yielding information on the structure in which they are arranged in the module. We derive subgroups of A8 by considering stabilizers of n-tuples derived from partitions of eight letters, and develop their representation theory over a field of characteristic 2, relying heavily on methods of passing information to groups from their subgroups, with special attention toward obtaining the Loewy structure of their projective indecomposable representations.
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Date Issued
1993
PURL
http://purl.flvc.org/fcla/dt/14971
Subject Headings
Representations of groups, Projective modules (Algebra), Indecomposable modules
Format
Document (PDF)
Representation of groups in quantum mechanics
Title
Representation of groups in quantum mechanics.
Creator
Paskaleva, Elitza Dimitrova, Florida Atlantic University, Schroeck, Franklin E., Department of Mathematical Sciences, Charles E. Schmidt College of Science
Abstract/Description
In this work, we discuss the conceptual framework of quantum mechanics in the Hilbert space formalism from a group representation point of view. After a brief review of the main results of the theory of groups and their representations, we describe mathematical models of the subject, and show the applications of this theory for getting numerical answers to problems in elementary particle physics.
Date Issued
2000
PURL
http://purl.flvc.org/fcla/dt/15758
Subject Headings
Quantum theory, Particles (Nuclear physics), Representations of groups, Hilbert space
Format
Document (PDF)
Fuzzy identification of processes on finite training sets with known features
Title
Fuzzy identification of processes on finite training sets with known features.
Creator
Diaz-Robainas, Regino R., Florida Atlantic University, Huang, Ming Z., Zilouchian, Ali, College of Engineering and Computer Science, Department of Computer and Electrical Engineering and Computer Science
Abstract/Description
A methodology is presented to construct an approximate fuzzy-mapping algorithm that maps multiple inputs to single outputs given a finite training set of argument vectors functionally linked to corresponding scalar outputs. Its scope is limited to problems where the features are known in advance, or equivalently, where the expected functional representation is known to depend exclusively on the known selected variables. Programming and simulations to implement the methodology make use of...
Show moreA methodology is presented to construct an approximate fuzzy-mapping algorithm that maps multiple inputs to single outputs given a finite training set of argument vectors functionally linked to corresponding scalar outputs. Its scope is limited to problems where the features are known in advance, or equivalently, where the expected functional representation is known to depend exclusively on the known selected variables. Programming and simulations to implement the methodology make use of Matlab Fuzzy and Neural toolboxes and a PC application of Prolog, and applications range from approximate representations of the direct kinematics of parallel manipulators to fuzzy controllers.
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Date Issued
1996
PURL
http://purl.flvc.org/fcla/dt/12487
Subject Headings
Fuzzy algorithms, Set theory, Logic, Symbolic and mathematical, Finite groups, Representations of groups
Format
Document (PDF)
Subgroups of bounded Abelian groups
Title
Subgroups of bounded Abelian groups.
Creator
Petroro, Carla., Florida Atlantic University, Schmidmeier, Markus
Abstract/Description
Birkhoff raised the question of how to determine "relative invariants of subgroups" of a given group. Let us consider pairs (A, B ) where B is a finite pn-bounded Abelian group and A is a subgroup of B. Maps between pairs (A, B) --> (A', B') are morphisms f : B --> B' such that f (A) --> A'. Classification of such pairs, up to isomorphism, is Birkhoff's famous problem. By the Krull-Remak-Schmidt theorem, an arbitrary pair (A, B) is a direct sum of indecomposable pairs, and the multiplicities...
Show moreBirkhoff raised the question of how to determine "relative invariants of subgroups" of a given group. Let us consider pairs (A, B ) where B is a finite pn-bounded Abelian group and A is a subgroup of B. Maps between pairs (A, B) --> (A', B') are morphisms f : B --> B' such that f (A) --> A'. Classification of such pairs, up to isomorphism, is Birkhoff's famous problem. By the Krull-Remak-Schmidt theorem, an arbitrary pair (A, B) is a direct sum of indecomposable pairs, and the multiplicities of the indecomposables are determined uniquely. The purpose of this thesis is to describe the decomposition of such pairs, (A, B), explicitly for n = 2 and n = 3. We describe explicitly how an indecomposable pair can possibly embed into a given pair (A, B). This construction gives rise to formulas for the multiplicity of an indecomposable in the direct sum decomposition of the pair (A, B). These decomposition numbers form a full set of relative invariant, as requested by Birkhoff.
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Date Issued
2004
PURL
http://purl.flvc.org/fcla/dt/13118
Subject Headings
Abelian groups, Modules (Algebra), Indecomposable modules, Representations of groups, Algebras, Linear
Format
Document (PDF)
Auslander-Reiten theory for systems of submodule embeddings
Title
Auslander-Reiten theory for systems of submodule embeddings.
Creator
Moore, Audrey., Charles E. Schmidt College of Science, Department of Mathematical Sciences
Abstract/Description
In this dissertation, we will investigate aspects of Auslander-Reiten theory adapted to the setting of systems of submodule embeddings. Using this theory, we can compute Auslander-Reiten quivers of such categories, which among other information, yields valuable information about the indecomposable objects in such a category. A main result of the dissertation is an adaptation to this situation of the Auslander and Ringel-Tachikawa Theorem which states that for an artinian ring R of finite...
Show moreIn this dissertation, we will investigate aspects of Auslander-Reiten theory adapted to the setting of systems of submodule embeddings. Using this theory, we can compute Auslander-Reiten quivers of such categories, which among other information, yields valuable information about the indecomposable objects in such a category. A main result of the dissertation is an adaptation to this situation of the Auslander and Ringel-Tachikawa Theorem which states that for an artinian ring R of finite representation type, each R-module is a direct sum of finite-length indecomposable R-modules. In cases where this applies, the indecomposable objects obtained in the Auslander-Reiten quiver give the building blocks for the objects in the category. We also briefly discuss in which cases systems of submodule embeddings form a Frobenius category, and for a few examples explore pointwise Calabi-Yau dimension of such a category.
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Date Issued
2009
PURL
http://purl.flvc.org/fcla/dt/210496
Subject Headings
Artin algebras, Rings (Algebra), Representation of algebras, Embeddings (Mathematics), Linear algebraic groups
Format
Document (PDF)