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Title:

On Lie algebras in braided categories

Description:

the concepts of Lie super and Lie color algebras. Our Lie algebras have n-ary multiplications between various graded components. They possess universal enveloping algebras that are Hopf algebras in the given category. Their biproducts with the group ring are noncommutative noncocommutative Hopf algebras some of them known in the literature. Conv...

the concepts of Lie super and Lie color algebras. Our Lie algebras have n-ary multiplications between various graded components. They possess universal enveloping algebras that are Hopf algebras in the given category. Their biproducts with the group ring are noncommutative noncocommutative Hopf algebras some of them known in the literature. Conversely the primitive elements of a Hopf algebra Minimize

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The Pennsylvania State University CiteSeerX Archives

Year of Publication:

2013-02-01

Source:

http://arxiv.org/pdf/q-alg/9612002v1.pdf

http://arxiv.org/pdf/q-alg/9612002v1.pdf Minimize

Document Type:

text

Language:

en

Subjects:

Graded Lie algebra ; braided category ; braided Hopf algebra ; universal enveloping

Graded Lie algebra ; braided category ; braided Hopf algebra ; universal enveloping Minimize

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Metadata may be used without restrictions as long as the oai identifier remains attached to it.

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Title:

On Lie Algebras in the Category of Yetter-Drinfeld Modules

Description:

the primitive elements of H do not form an ordinary Lie algebra anymore. We introduce the notion of a (generalized) Lie algebra in YDK K such that the set of primitive elements P(H) is a Lie algebra in this sense. Also the Yetter-Drinfeld module of derivations of an algebra A in YDK K is a Lie algebra. Furthermore for each Lie algebra in YDK K t...

the primitive elements of H do not form an ordinary Lie algebra anymore. We introduce the notion of a (generalized) Lie algebra in YDK K such that the set of primitive elements P(H) is a Lie algebra in this sense. Also the Yetter-Drinfeld module of derivations of an algebra A in YDK K is a Lie algebra. Furthermore for each Lie algebra in YDK K there is a universal enveloping algebra which turns out to be a Hopf algebra in YDK K. Minimize

Contributors:

The Pennsylvania State University CiteSeerX Archives

Year of Publication:

2013-02-01

Source:

http://arxiv.org/pdf/q-alg/9612023v1.pdf

http://arxiv.org/pdf/q-alg/9612023v1.pdf Minimize

Document Type:

text

Language:

en

Subjects:

braided category ; Yetter-Drinfeld module ; Lie algebra ; universal

braided category ; Yetter-Drinfeld module ; Lie algebra ; universal Minimize

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Metadata may be used without restrictions as long as the oai identifier remains attached to it.

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Title:

1 UPDATE SCHEDULES OF SEQUENTIAL DYNAMICAL SYSTEMS

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Abstract. Sequential dynamical systems have the property, that the updates of states of individual cells occur sequentially, so that the global update of the system depends on the order of the individual updates. This order is given by an order on the set of vertices of the dependency graph. It turns out that only a partial suborder is necessary...

Abstract. Sequential dynamical systems have the property, that the updates of states of individual cells occur sequentially, so that the global update of the system depends on the order of the individual updates. This order is given by an order on the set of vertices of the dependency graph. It turns out that only a partial suborder is necessary to describe the global update. This paper defines and studies this partial order and its influence on the global update function. Minimize

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The Pennsylvania State University CiteSeerX Archives

Year of Publication:

2008-07-01

Source:

http://www.mathematik.uni-muenchen.de/~pareigis/Papers/USSDS_FI.PDF

http://www.mathematik.uni-muenchen.de/~pareigis/Papers/USSDS_FI.PDF Minimize

Document Type:

text

Language:

en

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Metadata may be used without restrictions as long as the oai identifier remains attached to it.

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Title:

Four lectures on Hopf algebras

Publisher:

Ludwig-Maximilians-Universität München

Contributors:

Pareigis, Bodo

Year of Publication:

1984-01-01

Document Type:

doc-type:book ; Monographie ; NonPeerReviewed

Subjects:

Mathematik ; Informatik und Statistik ; ddc:510

Mathematik ; Informatik und Statistik ; ddc:510 Minimize

Relations:

Pareigis, Bodo (1984): Four lectures on Hopf algebras. Barcelona: Barcelona

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Title:

Analytische und Projektive Geometrie für die Computer-Graphik

Publisher:

Ludwig-Maximilians-Universität München

Contributors:

Pareigis, Bodo

Year of Publication:

1990-01-01

Document Type:

doc-type:book ; Monographie ; NonPeerReviewed

Subjects:

Mathematik ; Informatik und Statistik ; ddc:510

Mathematik ; Informatik und Statistik ; ddc:510 Minimize

Relations:

http://epub.ub.uni-muenchen.de/7122/1/7122.pdf ; Pareigis, Bodo (1990): Analytische und Projektive Geometrie für die Computer-Graphik. Stuttgart: Teubner

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Title:

On Lie Algebras in the Category of Yetter-Drinfeld Modules

Description:

The category of Yetter-Drinfeld modules over a Hopf algebra (with bijektive antipode over a field) is a braided monoidal category. Given a Hopf algebra in this category then the primitive elements of this Hopf algebra do not form an ordinary Lie algebra anymore. We introduce the notion of a (generalized) Lie algebra in the category of Yetter-Dri...

The category of Yetter-Drinfeld modules over a Hopf algebra (with bijektive antipode over a field) is a braided monoidal category. Given a Hopf algebra in this category then the primitive elements of this Hopf algebra do not form an ordinary Lie algebra anymore. We introduce the notion of a (generalized) Lie algebra in the category of Yetter-Drinfeld modules such that the set of primitive elements of a Hopf algebra is a Lie algebra in this sense. It has n-ary partially defined Lie multiplications on certain symmetric submodules of n- fold tensor products. They satisfy antisymmetry and Jacobi identities. Also the Yetter-Drinfeld module of derivations of an associative algebra in the category of Yetter- Drinfeld modules is a Lie algebra. Furthermore for each Lie algebra in the category of Yetter-Drinfeld modules there is a universal enveloping algebra which turns out to be a (braided) Hopf algebra in this category. ; Comment: 21 pages, NLaTeX with bezier.sty, amsart.sty Minimize

Year of Publication:

1996-12-17

Document Type:

text

Subjects:

Mathematics - Quantum Algebra

Mathematics - Quantum Algebra Minimize

DDC:

512 Algebra *(computed)*

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Title:

On Lie Algebras in Braided Categories

Description:

The set of primitive elements of a Hopf algebra in the braided category of group graded vector spaces (with a commutative group) carry the structure of a generalized Lie algebra. In particular the graded derivations of an associative algebra carry this Lie algebra structure. The Lie multiplications consist of certain n-ary partially defined mult...

The set of primitive elements of a Hopf algebra in the braided category of group graded vector spaces (with a commutative group) carry the structure of a generalized Lie algebra. In particular the graded derivations of an associative algebra carry this Lie algebra structure. The Lie multiplications consist of certain n-ary partially defined multiplications satisfying generalized antisymmetry and Jacobi identities. This generalizes the concept of Lie super algebras and Lie color algebras. We show that universal enveloping algebras in the braided category exist. They are (braided) Hopf algebras. This explains many constructions of noncommutative noncocommutative Hopf algebras in the literature. ; Comment: 20 pages - uses nlatex = NFSS Latex plus AMS macro package amsart.sty Minimize

Year of Publication:

1996-12-01

Document Type:

text

Subjects:

Mathematics - Quantum Algebra

Mathematics - Quantum Algebra Minimize

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Title:

Reconstruction of Hidden Symmetries

Description:

Representations of a group $G$ in vector spaces over a field $K$ form a category. One can reconstruct the given group $G$ from its representations to vector spaces as the full group of monoidal automorphisms of the underlying functor. This is a special example of Tannaka-Krein theory. This theory was used in recent years to reconstruct quantum g...

Representations of a group $G$ in vector spaces over a field $K$ form a category. One can reconstruct the given group $G$ from its representations to vector spaces as the full group of monoidal automorphisms of the underlying functor. This is a special example of Tannaka-Krein theory. This theory was used in recent years to reconstruct quantum groups (quasitriangular Hopf algebras) in the study of algebraic quantum field theory and other applications. We show that a similar study of representations in spaces with additional structure (super vector spaces, graded vector spaces, comodules, braided monoidal categories) produces additional symmetries, called ``hidden symmetries''. More generally, reconstructed quantum groups tend to decompose into a smash product of the given quantum group and a quantum group of ``hidden'' symmetries of the base category. ; Comment: 42 pages, amslatex, figures generated with bezier.sty, replaced to facilitate mailing Minimize

Year of Publication:

1994-12-09

Document Type:

text

Subjects:

High Energy Physics - Theory

High Energy Physics - Theory Minimize

DDC:

512 Algebra *(computed)*

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Title:

Descent theory applied to Galois theory

Publisher:

Ludwig-Maximilians-Universität München

Year of Publication:

1986-01-01

Document Type:

doc-type:book ; Monographie ; NonPeerReviewed

Subjects:

Mathematik ; Informatik und Statistik ; ddc:510

Mathematik ; Informatik und Statistik ; ddc:510 Minimize

Relations:

Pareigis, Bodo (1986): Descent theory applied to Galois theory. Department of Math, University of California: San Diego

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Title:

Endliche Hopf-Algebren

Publisher:

Ludwig-Maximilians-Universität München

Year of Publication:

1973-01-01

Document Type:

doc-type:book ; Monographie ; NonPeerReviewed

Subjects:

Mathematik ; Informatik und Statistik ; ddc:510

Mathematik ; Informatik und Statistik ; ddc:510 Minimize

Relations:

http://epub.ub.uni-muenchen.de/7311/1/7311.pdf ; Pareigis, Bodo (1973): Endliche Hopf-Algebren. Vorlesungsausarbeitung. München: UNI-Druck

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