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- Manin_matrix abstract "In mathematics, Manin matrices, named after Yuri Manin who introduced them around 1987–88, are a class of matrices with elements in a not-necessarily commutative ring, which in a certain sense behave like matrices whose elements commute. In particular there is natural definition of the determinant for them and most linear algebra theorems like Cramer's rule, Cayley–Hamilton theorem, etc. hold true for them. Any matrix with commuting elements is a Manin matrix. These matrices have applications in representation theory in particular to Capelli's identity, Yangian and quantum integrable systems.Manin matrices are particular examples of Manin's general constructionof "non-commutative symmetries" which can be applied to any algebra.From this point of view they are "non-commutative endomorphisms"of polynomial algebra C[x1, ...xn].Taking (q)-(super)-commuting variables one will get (q)-(super)-analogsof Manin matrices, which are closely related to quantum groups. Maninworks were influenced by the quantum group theory.He discovered that quantized algebra of functions Funq(GL)can be definedby the requirement that T and Tt are simultaneouslyq-Manin matrices.In that sense it should be stressed that (q)-Manin matrices are definedonly by half of the relations of related quantum group Funq(GL), and these relations are enough for many linear algebra theorems.".
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- Manin_matrix wikiPageRevisionID "671238368".
- Manin_matrix wikiPageWikiLink Abelianization.
- Manin_matrix wikiPageWikiLink Adjugate_matrix.
- Manin_matrix wikiPageWikiLink Berezinian.
- Manin_matrix wikiPageWikiLink Bethe_ansatz.
- Manin_matrix wikiPageWikiLink Bialgebra.
- Manin_matrix wikiPageWikiLink Capelli_determinant.
- Manin_matrix wikiPageWikiLink Capelli_identity.
- Manin_matrix wikiPageWikiLink Capellis_identity.
- Manin_matrix wikiPageWikiLink Category:Matrices.
- Manin_matrix wikiPageWikiLink Category:Matrix_theory.
- Manin_matrix wikiPageWikiLink Cayley-Hamilton_theorem.
- Manin_matrix wikiPageWikiLink Cayley–Hamilton_theorem.
- Manin_matrix wikiPageWikiLink Coalgebra.
- Manin_matrix wikiPageWikiLink Coassociative.
- Manin_matrix wikiPageWikiLink Commutative_property.
- Manin_matrix wikiPageWikiLink Commutativity.
- Manin_matrix wikiPageWikiLink Commutator.
- Manin_matrix wikiPageWikiLink Commutator_subgroup.
- Manin_matrix wikiPageWikiLink Cramers_rule.
- Manin_matrix wikiPageWikiLink Determinant.
- Manin_matrix wikiPageWikiLink Dieudonné_determinant.
- Manin_matrix wikiPageWikiLink Dominique_Foata.
- Manin_matrix wikiPageWikiLink Exterior_algebra.
- Manin_matrix wikiPageWikiLink Grassmann_algebra.
- Manin_matrix wikiPageWikiLink Integrable_system.
- Manin_matrix wikiPageWikiLink Linear_algebra.
- Manin_matrix wikiPageWikiLink MacMahon_Master_theorem.
- Manin_matrix wikiPageWikiLink Mathematics.
- Manin_matrix wikiPageWikiLink Matrix_(mathematics).
- Manin_matrix wikiPageWikiLink Newton_identities.
- Manin_matrix wikiPageWikiLink Newtons_identities.
- Manin_matrix wikiPageWikiLink Non-commutative_geometry.
- Manin_matrix wikiPageWikiLink Noncommutative_geometry.
- Manin_matrix wikiPageWikiLink Permutation.
- Manin_matrix wikiPageWikiLink Pierre_Cartier_(mathematician).
- Manin_matrix wikiPageWikiLink Quantum_group.
- Manin_matrix wikiPageWikiLink Quasideterminant.
- Manin_matrix wikiPageWikiLink Representation_theory.
- Manin_matrix wikiPageWikiLink Ring_(mathematics).
- Manin_matrix wikiPageWikiLink Schur_complement.
- Manin_matrix wikiPageWikiLink Universal_enveloping_algebra.
- Manin_matrix wikiPageWikiLink Yangian.
- Manin_matrix wikiPageWikiLink Yuri_I._Manin.
- Manin_matrix wikiPageWikiLinkText "Manin matrix".
- Manin_matrix hasPhotoCollection Manin_matrix.
- Manin_matrix wikiPageUsesTemplate Template:ArXiv.
- Manin_matrix wikiPageUsesTemplate Template:Cite_book.
- Manin_matrix wikiPageUsesTemplate Template:Cite_journal.
- Manin_matrix wikiPageUsesTemplate Template:Cite_paper.
- Manin_matrix wikiPageUsesTemplate Template:Reflist.
- Manin_matrix subject Category:Matrices.
- Manin_matrix subject Category:Matrix_theory.
- Manin_matrix hypernym Matrices.
- Manin_matrix type Article.
- Manin_matrix type Article.
- Manin_matrix type Matrix.
- Manin_matrix comment "In mathematics, Manin matrices, named after Yuri Manin who introduced them around 1987–88, are a class of matrices with elements in a not-necessarily commutative ring, which in a certain sense behave like matrices whose elements commute. In particular there is natural definition of the determinant for them and most linear algebra theorems like Cramer's rule, Cayley–Hamilton theorem, etc. hold true for them. Any matrix with commuting elements is a Manin matrix.".
- Manin_matrix label "Manin matrix".
- Manin_matrix sameAs m.0k8y74y.
- Manin_matrix sameAs Q17098697.
- Manin_matrix sameAs Q17098697.
- Manin_matrix wasDerivedFrom Manin_matrix?oldid=671238368.
- Manin_matrix isPrimaryTopicOf Manin_matrix.