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1 
An infinite family of anticommutative algebras with a cubic formSchoenecker, Kevin J. January 2007 (has links)
Thesis (Ph. D.)Ohio State University, 2007. / Title from first page of PDF file. Includes bibliographical references (p. 56).

2 
On the tensor products of JCalgebras and JWalgebrasJamjoom, Fatmah B. January 1990 (has links)
No description available.

3 
On Jordan and associative ringsSmith, Kirby C. January 1969 (has links)
Thesis (Ph. D.)University of WisconsinMadison, 1969. / Typescript. Vita. eContent providerneutral record in process. Description based on print version record. Includes bibliographical references.

4 
3dimensional symplectic geometries and metasymplectic geometriesChung, KW. January 1989 (has links)
No description available.

5 
Homological properties of finitedimensional algebrasMembrilloHernandez, Fausto Humberto January 1993 (has links)
No description available.

6 
Spectral functions and smoothing techniques on Jordan algebrasBaes, Michel 22 September 2006 (has links)
Successful methods for a large class of nonlinear convex optimization problems have recently been developed. This class, known as selfscaled optimization problems, has been defined by Nesterov and Todd in 1994. As noticed by Guler in 1996, this class is best described using an algebraic structure known as Euclidean Jordan algebra, which provides an elegant and powerful unifying framework for its study. Euclidean Jordan algebras are now a popular setting for the analysis of algorithms designed for selfscaled optimization problems : dozens of research papers in optimization deal explicitely with them.
This thesis proposes an extensive and selfcontained description of Euclidean Jordan algebras, and shows how they can be used to design and analyze new algorithms for selfscaled optimization.
Our work focuses on the socalled spectral functions on Euclidean Jordan algebras, a natural generalization of spectral functions of symmetric matrices. Based on an original variational analysis technique for Euclidean Jordan algebras, we discuss their most important properties, such as differentiability and convexity. We show how these results can be applied in order to extend several algorithms existing for linear or secondorder programming to the general class of selfscaled problems. In particular, our methods allowed us to extend to some nonlinear convex problems the powerful smoothing techniques of Nesterov, and to demonstrate its excellent theoretical and practical efficiency.

7 
Group decompositions, Jordan algebras, and algorithms for pgroups /Wilson, James B., January 2008 (has links)
Thesis (Ph. D.)University of Oregon, 2008. / Typescript. Includes vita and abstract. Includes bibliographical references (leaves 121125). Also available online in Scholars' Bank; and in ProQuest, free to University of Oregon users.

8 
Deformações e isotopias de álgebras de Jordan / Deformations and isotopies of Jordan algebrasMartin, Maria Eugenia 04 September 2013 (has links)
Neste trabalho apresentamos a classificação algébrica e geométrica das álgebras de Jordan de dimensões pequenas sobre um corpo $k$ algebricamente fechado de $char k eq 2$ e sobre o corpo dos números reais. A classificação algébrica foi realizada de duas maneiras: a menos de isomorfismos e a menos de isotopias. Enquanto que a classificação geométrica foi feita estudando as variedades de álgebras de Jordan $Jor_$ para $n \\leq 4$ e $JorR_$ para $n\\leq 3$. Provamos que $Jor_$ tem 73 órbitas sob a ação de $GL(V)$ e que é a união dos fechos de Zariski das órbitas de 10 álgebras rígidas, cada um dos quais corresponde a uma componente irredutível. Analogamente, mostramos que $JorR_$ tem 26 órbitas e é a união dos fechos de Zariski das órbitas de 8 álgebras rígidas. Também obtivemos que o número de componentes irredutíveis em $Jor_$ é $\\geq 26$. Construímos ainda três famílias de álgebras rígidas não associativas, não semisimples e indecomponíveis as quais correspondem a componentes irredutíveis de $Jor_$ e $JorR_$ para todo $n\\geq 5$. / In this work we present the algebraic and geometric classification of Jordan algebras of small dimensions over an algebraically closed field $k$ of $char k eq 2$ and over the field of real numbers. The algebraic classification was accomplished in two ways: up to isomorphism and up to isotopy. On the other hand, the geometric classification was obtained studying the varieties of Jordan algebras $Jor_$ for $n\\leq4$ and $JorR_$ for $n\\leq3$. We prove that $Jor_$ has 73 orbits under the action of $GL(V)$ and it is the union of Zariski closures of the orbits of 10 rigid algebras, each of which corresponds to one irreducible component. Analogously, we show that $JorR_$ has 26 orbits and is the union of Zariski closures of the orbits of 8 rigid algebras. Also we obtain that the number of irreducible components in $Jor_$ is $\\geq26$. We construct three families of indecomposable nonsemisimple, nonassociative rigid algebras which for any $n\\geq5$, correspond to irreducible components of $Jor_$ and $JorR_$.

9 
Structure and representation of real locally C* and locally JBalgebrasFriedman, Oleg 08 1900 (has links)
The abstract Banach associative symmetrical *algebras over C, so called C*
algebras, were introduced first in 1943 by Gelfand and Naimark24. In the present time
the theory of C*algebras has become a vast portion of functional analysis having connections
and applications in almost all branches of modern mathematics and theoretical
physics.
From the 1940’s and the beginning of 1950’s there were numerous attempts made
to extend the theory of C*algebras to a category wider than Banach algebras. For example,
in 1952, while working on the theory of locallymultiplicativelyconvex algebras
as projective limits of projective families of Banach algebras, Arens in the paper8 and
Michael in the monograph48 independently for the first time studied projective limits
of projective families of functional algebras in the commutative case and projective
limits of projective families of operator algebras in the noncommutative case. In 1971
Inoue in the paper33 explicitly studied topological *algebras which are topologically
isomorphic to projective limits of projective families of C*algebras and obtained their
basic properties. He as well suggested a name of locally C*algebras for that category.
For the present state of the theory of locally C*algebras see the monograph of
Fragoulopoulou.
Also there were many attempts to extend the theory of C*algebras to nonassociative
algebras which are close in properties to associative algebras (in particular,
to Jordan algebras). In fact, the real Jordan analogues of C*algebras, so called JBalgebras, were first introduced in 1978 by Alfsen, Shultz and Størmer in1. One of the
main results of the aforementioned paper stated that modulo factorization over a unique
Jordan ideal each JBalgebra is isometrically isomorphic to a JCalgebra, i.e. an operator
norm closed Jordan subalgebra of the Jordan algebra of all bounded selfadjoint
operators with symmetric multiplication acting on a complex Hilbert space.
Projective limits of Banach algebras have been studied sporadically by many
authors since 1952, when they were first introduced by Arens8 and Michael48. Projective
limits of complex C*algebras were first mentioned by Arens. They have since been
studied under various names by Wenjen, Sya DoShin, Brooks, Inoue, Schmüdgen,
Fritzsche, Fragoulopoulou, Phillips, etc.
We will follow Inoue33 in the usage of the name "locally C*algebras" for these
objects.
At the same time, in parallel with the theory of complex C*algebras, a theory
of their real and Jordan analogues, namely real C*algebras and JBalgebras, has been
actively developed by various authors.
In chapter 2 we present definitions and basic theorems on complex and real
C*algebras, JBalgebras and complex locally C*algebras to be used further.
In chapter 3 we define a real locally Hilbert space HR and an algebra of operators
L(HR) (not bounded anymore) acting on HR.
In chapter 4 we give new definitions and study several properties of locally C*
and locally JBalgebras. Then we show that a real locally C*algebra (locally JBalgebra)
is locally isometric to some closed subalgebra of L(HR).
In chapter 5 we study complex and real Abelian locally C*algebras.
In chapter 6 we study universal enveloping algebras for locally JBalgebras.
In chapter 7 we define and study dual space characterizations of real locally C*
and locally JBalgebras.
In chapter 8 we define barreled real locally C* and locally JBalgebras and study
their representations as unbounded operators acting on dense subspaces of some Hilbert
spaces.
It is beneficial to extend the existing theory to the case of real and Jordan
analogues of complex locally C*algebras. The present thesis is devoted to study such
analogues, which we call real locally C* and locally JBalgebras. / Mathematics / D. Phil. (Mathematics)

10 
Deformações e isotopias de álgebras de Jordan / Deformations and isotopies of Jordan algebrasMaria Eugenia Martin 04 September 2013 (has links)
Neste trabalho apresentamos a classificação algébrica e geométrica das álgebras de Jordan de dimensões pequenas sobre um corpo $k$ algebricamente fechado de $char k eq 2$ e sobre o corpo dos números reais. A classificação algébrica foi realizada de duas maneiras: a menos de isomorfismos e a menos de isotopias. Enquanto que a classificação geométrica foi feita estudando as variedades de álgebras de Jordan $Jor_$ para $n \\leq 4$ e $JorR_$ para $n\\leq 3$. Provamos que $Jor_$ tem 73 órbitas sob a ação de $GL(V)$ e que é a união dos fechos de Zariski das órbitas de 10 álgebras rígidas, cada um dos quais corresponde a uma componente irredutível. Analogamente, mostramos que $JorR_$ tem 26 órbitas e é a união dos fechos de Zariski das órbitas de 8 álgebras rígidas. Também obtivemos que o número de componentes irredutíveis em $Jor_$ é $\\geq 26$. Construímos ainda três famílias de álgebras rígidas não associativas, não semisimples e indecomponíveis as quais correspondem a componentes irredutíveis de $Jor_$ e $JorR_$ para todo $n\\geq 5$. / In this work we present the algebraic and geometric classification of Jordan algebras of small dimensions over an algebraically closed field $k$ of $char k eq 2$ and over the field of real numbers. The algebraic classification was accomplished in two ways: up to isomorphism and up to isotopy. On the other hand, the geometric classification was obtained studying the varieties of Jordan algebras $Jor_$ for $n\\leq4$ and $JorR_$ for $n\\leq3$. We prove that $Jor_$ has 73 orbits under the action of $GL(V)$ and it is the union of Zariski closures of the orbits of 10 rigid algebras, each of which corresponds to one irreducible component. Analogously, we show that $JorR_$ has 26 orbits and is the union of Zariski closures of the orbits of 8 rigid algebras. Also we obtain that the number of irreducible components in $Jor_$ is $\\geq26$. We construct three families of indecomposable nonsemisimple, nonassociative rigid algebras which for any $n\\geq5$, correspond to irreducible components of $Jor_$ and $JorR_$.

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