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Noncommutative algebras related with Schubert calculus on Coxeter groups
 Europian Journ. of Combin
"... For any finite Coxeter system (W, S) we construct a certain noncommutative algebra, socalled bracket algebra, together with a familiy of commuting elements, socalled Dunkl elements. Dunkl elements conjecturally generate an algebra which is canonically isomorphic to the coinvariant algebra of the g ..."
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Cited by 12 (4 self)
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For any finite Coxeter system (W, S) we construct a certain noncommutative algebra, socalled bracket algebra, together with a familiy of commuting elements, socalled Dunkl elements. Dunkl elements conjecturally generate an algebra which is canonically isomorphic to the coinvariant algebra
NONCOMMUTATIVE ALGEBRAIC GEOMETRY: A SURVEY OF THE APPROACH VIA SHEAVES ON NONCOMMUTATIVE SPACES
"... To me noncommutative algebraic geometry came from the consideration of noncommutative spaces defined in terms of notions like: noncommutative valuations and pseudovaluations, primes in algebras, prime ideals of Noetherian rings or prime torsion theories for rings or categories. The root of the the ..."
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To me noncommutative algebraic geometry came from the consideration of noncommutative spaces defined in terms of notions like: noncommutative valuations and pseudovaluations, primes in algebras, prime ideals of Noetherian rings or prime torsion theories for rings or categories. The root
Topics in Noncommutative Algebraic Geometry, Homological Algebra and Ktheory.
"... This text is based on my lectures delivered at the School on Algebraic KTheory and Applications which took place at the International Center for Theoretical Physics (ICTP) in Trieste during the last two weeks of May of 2007. It might be regarded as an introduction to some basic facts of noncommutat ..."
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Cited by 4 (0 self)
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of noncommutative algebraic geometry and the related
Topological expansion of the Bethe ansatz, and noncommutative algebraic geometry
 JHEP 0903, 094 (2009) [arXiv:0809.3367 [mathph
"... HAL is a multidisciplinary open access archive for the deposit and dissemination of scientific research documents, whether they are published or not. The documents may come from teaching and research institutions in France or abroad, or from public or private research centers. L’archive ouverte p ..."
Quantum Teichmüller space as a noncommutative algebraic object
, 2008
"... We consider the quantum Teichmüller space of the punctured surface introduced by ChekhovFockKashaev, and formalize it as a noncommutative deformation of the space of algebraic functions on the Teichmüller space of the surface. In order to apply it in 3dimensional topology, we put more attention ..."
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Cited by 15 (4 self)
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We consider the quantum Teichmüller space of the punctured surface introduced by ChekhovFockKashaev, and formalize it as a noncommutative deformation of the space of algebraic functions on the Teichmüller space of the surface. In order to apply it in 3dimensional topology, we put more
Exploring noncommutative algebras via deformation theory
, 2005
"... In this lecture I would like to address the following question: given an associative algebra A0, what are the possible ways to deform it? Consideration of this question for concrete algebras often leads to interesting mathematical discoveries. I will discuss several approaches to this question, and ..."
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Cited by 6 (0 self)
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In this lecture I would like to address the following question: given an associative algebra A0, what are the possible ways to deform it? Consideration of this question for concrete algebras often leads to interesting mathematical discoveries. I will discuss several approaches to this question
Prelude: Arithmetic Fundamental Groups and Noncommutative Algebra
 PROCEEDINGS OF SYMPOSIA IN PURE MATHEMATICS
"... From number theory to string theory, analyzing algebraic relations in two variables still dominates how we view laws governing relations between quantities. An algebraic relation between two variables defines a nonsingular projective curve. Our understanding starts with moduli of curves. From, how ..."
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Cited by 6 (4 self)
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From number theory to string theory, analyzing algebraic relations in two variables still dominates how we view laws governing relations between quantities. An algebraic relation between two variables defines a nonsingular projective curve. Our understanding starts with moduli of curves. From
PROJECTIVE RESOLUTION OF MODULES OVER THE NONCOMMUTATIVE ALGEBRA
, 2009
"... We give an explicit algorithm to compute a projective resolution of a module over the noncommutative ring based on the noncommutative Gröbner bases theory. ..."
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We give an explicit algorithm to compute a projective resolution of a module over the noncommutative ring based on the noncommutative Gröbner bases theory.
Results 11  20
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3,031