The Experts below are selected from a list of 37299 Experts worldwide ranked by ideXlab platform
Feng-xiao Wang - One of the best experts on this subject based on the ideXlab platform.
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T-Fuzzy Subalgebras and T-Fuzzy Ideals of BCH-Algebras
2008 3rd International Conference on Innovative Computing Information and Control, 2008Co-Authors: Feng-xiao WangAbstract:The aim of this paper is to introduce the notions of T-fuzzy Subalgebras and T-fuzzy ideals of BCH-algebras and to investigate their properties. We give several characterizations of T-fuzzy Subalgebras and T-fuzzy ideals. The relations among various fuzzy Subalgebras and ideals are discussed as well. Finally, we characterize well BCH-algebras via T-fuzzy Subalgebras.
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On Rough Ideals and Rough Fuzzy Ideals of BCI-Algebras
2008 Fifth International Conference on Fuzzy Systems and Knowledge Discovery, 2008Co-Authors: Lu Chen, Feng-xiao WangAbstract:Based on rough set theory, we study the mathematical structure of BCI-algebras. The lower and upper rough Subalgebras, the upper and lower rough ideals of BCI-algebras are defined. Then the properties of rough Subalgebras and rough ideals are discussed. The left and the right rough fuzzy ideals and Subalgebras are defined and researched.
Stefan Kolb - One of the best experts on this subject based on the ideXlab platform.
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homogeneous right coideal Subalgebras of quantized enveloping algebras
Bulletin of The London Mathematical Society, 2012Co-Authors: I Heckenberger, Stefan KolbAbstract:For a quantized enveloping algebra of a complex semisimple Lie algebra with deformation parameter not a root of unity, we classify all homogeneous right coideal Subalgebras. Any such right coideal subalgebra is determined uniquely by a triple consisting of two elements of the Weyl group and a subset of the set of simple roots satisfying some natural conditions. The essential ingredients of the proof are the Lusztig automorphisms and the classification of homogeneous right coideal Subalgebras of the Borel Hopf Subalgebras of quantized enveloping algebras obtained previously by H.-J. Schneider and the first named author. Key words: Quantum groups, coideal Subalgebras, Weyl group, weak order
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braid group actions on coideal Subalgebras of quantized enveloping algebras
Journal of Algebra, 2011Co-Authors: Stefan Kolb, Jacopo PellegriniAbstract:Abstract We construct braid group actions on coideal Subalgebras of quantized enveloping algebras which appear in the theory of quantum symmetric pairs. In particular, we construct an action of the semidirect product of Z n and the classical braid group in n strands on the coideal subalgebra corresponding to the symmetric pair ( sl 2 n ( C ) , sp 2 n ( C ) ) . This proves a conjecture by Molev and Ragoucy. We expect similar actions to exist for all symmetric simple complex Lie algebras. The given actions are inspired by Lusztigʼs braid group action on quantized enveloping algebras and are defined explicitly on generators. Braid group and algebra relations are verified with the help of the package Quagroup within the computer algebra program GAP .
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braid group actions on coideal Subalgebras of quantized enveloping algebras
arXiv: Quantum Algebra, 2011Co-Authors: Stefan Kolb, Jacopo PellegriniAbstract:We construct braid group actions on coideal Subalgebras of quantized enveloping algebras which appear in the theory of quantum symmetric pairs. In particular, we construct an action of the semidirect product of Z^n and the classical braid group in n strands on the coideal subalgebra corresponding to the symmetric pair (sl_{2n}(C), sp_{2n}(C)). This proves a conjecture by Molev and Ragoucy. We expect similar actions to exist for all symmetric Lie algebras. The given actions are inspired by Lusztig's braid group action on quantized enveloping algebras and are defined explicitly on generators. Braid group and algebra relations are verified with the help of the package Quagroup within the computer algebra program GAP.
Branimir Šešelja - One of the best experts on this subject based on the ideXlab platform.
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Fuzzy identities
2009 IEEE International Conference on Fuzzy Systems, 2009Co-Authors: Branimir Šešelja, Andreja TepavcevicAbstract:Fuzzy Subalgebras of a crisp algebra equipped with a compatible fuzzy equality are investigated. Fuzzy identities with respect to this fuzzy equality are considered. If a fuzzy subalgebra satisfies a fuzzy identity then the quotient cut-algebras over the corresponding cut-congruences fulfill the crisp version of the fuzzy identity. Particular cases of groupoid-like and similar algebras in this framework are also investigated.
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lattices of compatible relations satisfying a set of formulas
Algebra Universalis, 1998Co-Authors: Ivan Chajda, Branimir Šešelja, Andreja TepavcevicAbstract:The aim of the paper is to give a framework for the generation of algebraic lattices of compatible relations connected with algebras. These compatible relations satisfy a set of formulas (which can include symmetry and/or transitivity). A particular case are lattices elements of which are all relations reflexive on Subalgebras satisfying the same set of formulas, e.g., all tolerances, all quasi-orders, all congruences etc., on all Subalgebras of the given algebra (the subalgebra lattice being isomorphic with the ideal generated by the diagonal relation). Using the extension and intersection properties (a generalization of the CEP and the CIP), we give conditions under which these lattices satisfy a lattice identity, such as modularity and distributivity.
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Lattice of partially ordered fuzzy Subalgebras
Fuzzy Sets and Systems, 1996Co-Authors: Branimir ŠešeljaAbstract:Abstract Fuzzy Subalgebras are defined to be mappings from an algebra to a poset (which can be a lattice, and also the interval [0,1]), so that every level subset is an ordinary subalgebra. Every fuzzy subalgebra has a canonical representation, a mapping from the algebra to the poset of levels. Necessary and sufficient conditions under which a fuzzy subalgebra can be explicitly described by a suitable formula in lattice theoretic terms are given. Classes of algebras for which the poset of fuzzy Subalgebras is a lattice are characterized.
Jacopo Pellegrini - One of the best experts on this subject based on the ideXlab platform.
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braid group actions on coideal Subalgebras of quantized enveloping algebras
Journal of Algebra, 2011Co-Authors: Stefan Kolb, Jacopo PellegriniAbstract:Abstract We construct braid group actions on coideal Subalgebras of quantized enveloping algebras which appear in the theory of quantum symmetric pairs. In particular, we construct an action of the semidirect product of Z n and the classical braid group in n strands on the coideal subalgebra corresponding to the symmetric pair ( sl 2 n ( C ) , sp 2 n ( C ) ) . This proves a conjecture by Molev and Ragoucy. We expect similar actions to exist for all symmetric simple complex Lie algebras. The given actions are inspired by Lusztigʼs braid group action on quantized enveloping algebras and are defined explicitly on generators. Braid group and algebra relations are verified with the help of the package Quagroup within the computer algebra program GAP .
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braid group actions on coideal Subalgebras of quantized enveloping algebras
arXiv: Quantum Algebra, 2011Co-Authors: Stefan Kolb, Jacopo PellegriniAbstract:We construct braid group actions on coideal Subalgebras of quantized enveloping algebras which appear in the theory of quantum symmetric pairs. In particular, we construct an action of the semidirect product of Z^n and the classical braid group in n strands on the coideal subalgebra corresponding to the symmetric pair (sl_{2n}(C), sp_{2n}(C)). This proves a conjecture by Molev and Ragoucy. We expect similar actions to exist for all symmetric Lie algebras. The given actions are inspired by Lusztig's braid group action on quantized enveloping algebras and are defined explicitly on generators. Braid group and algebra relations are verified with the help of the package Quagroup within the computer algebra program GAP.
Karolina Vocke - One of the best experts on this subject based on the ideXlab platform.
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A Family of New Borel Subalgebras of Quantum Groups
Algebras and Representation Theory, 2020Co-Authors: Simon Lentner, Karolina VockeAbstract:We construct a family of right coideal Subalgebras of quantum groups, which have the property that all irreducible representations are one-dimensional, and which are maximal with this property. The obvious examples for this are the standard Borel Subalgebras expected from Lie theory, but in a quantum group there are many more. Constructing and classifying them is interesting for structural reasons, and because they lead to unfamiliar induced (Verma-)modules for the quantum group. The explicit family we construct in this article consists of quantum Weyl algebras combined with parts of a standard Borel subalgebra, and they have a triangular decomposition. Our main result is proving their Borel subalgebra property. Conversely we prove under some restrictions a classification result, which characterizes our family. Moreover we list for U _ q (_4) all possible triangular Borel Subalgebras, using our underlying results and additional by-hand arguments. This gives a good working example and puts our results into context.
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On Borel Subalgebras of quantum groups
arXiv: Quantum Algebra, 2019Co-Authors: Simon Lentner, Karolina VockeAbstract:For a quantum group, we study those right coideal Subalgebras, for which all irreducible representations are one-dimensional. If a right coideal subalgebra is maximal with this property, then we call it a Borel subalgebra. Besides the positive part of the quantum group and its reflections, we find new unfamiliar Borel Subalgebras, for example ones containing copies of the quantum Weyl algebra. Given a Borel subalgebra, we study its induced (Verma-)modules and prove among others that they have all irreducible finite-dimensional modules as quotients. We then give structural results using the graded algebra, which in particular leads to a conjectural formula for all triangular Borel Subalgebras, which we partly prove. As examples, we determine all Borel Subalgebras of $U_q(\mathfrak{sl}_2)$ and $U_q(\mathfrak{sl}_3)$ and discuss the induced modules.
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On right coideal Subalgebras of quantum groups
arXiv: Quantum Algebra, 2018Co-Authors: Karolina VockeAbstract:Right coideal Subalgebras are interesting substructures of Hopf algebras such as quantum groups. Examples of right coideal Subalgebras are the quantum Borel part as well as quantum symmetric pairs. Classifying right coideal Subalgebras is a difficult question with notable results by Schneider, Heckenberger and Kolb. After reviewing these results, as main result we prove that an arbitrary right coideal Subalgebras has a particularly nice set of generators. This allows in principle to specify the set of right coideal Subalgebras in a given case. As application we determine right coideal Subalgebras of the quantum groups Uq(sl2) and Uq(sl3) and discuss their representation theoretic properties.
