Poisson orders, symplectic reflection algebras and representation theory
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Publication:4418840
DOI10.1515/crll.2003.048zbMath1025.17007arXivmath/0201042OpenAlexW2963829412MaRDI QIDQ4418840
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Publication date: 12 August 2003
Published in: Journal für die reine und angewandte Mathematik (Crelles Journal) (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/math/0201042
Representations of orders, lattices, algebras over commutative rings (16G30) Poisson manifolds; Poisson groupoids and algebroids (53D17) Quantum groups (quantized function algebras) and their representations (20G42) Poisson algebras (17B63) Noetherian rings and modules (associative rings and algebras) (16P40)
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Poisson algebras via model theory and differential-algebraic geometry ⋮ Arc spaces and chiral symplectic cores ⋮ Azumaya loci and discriminant ideals of PI algebras ⋮ Poisson deformations of symplectic quotient singularities ⋮ DG Poisson algebra and its universal enveloping algebra ⋮ The Dixmier-Moeglin equivalence and a Gel’fand-Kirillov problem for Poisson polynomial algebras ⋮ Cuspidal Calogero-Moser and Lusztig families for Coxeter groups ⋮ Quantum traces and embeddings of stated skein algebras into quantum tori ⋮ Quantized Weyl algebras at roots of unity ⋮ Commutative bidifferential algebra ⋮ The number of independent Traces and Supertraces on the Symplectic Reflection Algebra H1, η (Γ ≀ S N ) ⋮ Noncommutative discriminants via Poisson primes ⋮ Universal enveloping algebras of Poisson Ore extensions ⋮ Suzuki functor at the critical level ⋮ Mapping class group representations derived from stated skein algebras ⋮ On the semi-centre of a Poisson algebra ⋮ Cluster algebra structures on Poisson nilpotent algebras ⋮ One dimensional representations of finite \(W\)-algebras, Dirac reduction and the orbit method ⋮ Poisson spectra in polynomial algebras ⋮ Computational aspects of Calogero-Moser spaces ⋮ Poisson orders on large quantum groups ⋮ Completions of symplectic reflection algebras. ⋮ On parabolic subgroups of symplectic reflection groups ⋮ Harish-Chandra bimodules for type A rational Cherednik algebras ⋮ Derived equivalences for a class of PI algebras ⋮ AUTOMORPHISMS AND SYMPLECTIC LEAVES OF CALOGERO–MOSER SPACES ⋮ A new linear quotient of \(\mathbf C^4\) admitting a symplectic resolution. ⋮ Dirac cohomology for symplectic reflection algebras ⋮ Reflection groups and rigidity of quadratic Poisson algebras ⋮ An analogue of the Kac-Weisfeiler conjecture ⋮ The Weyl algebra as a fixed ring ⋮ A counter-example to Martino's conjecture about generic Calogero-Moser families. ⋮ Cuspidal representations of rational Cherednik algebras at \(t=0\). ⋮ On the Dixmier-Moeglin equivalence for Poisson-Hopf algebras ⋮ On the importance of being primitive ⋮ Stratifications of Marsden-Weinstein reductions for representations of quivers and deformations of symplectic quotient singularities ⋮ On the Azumaya locus of almost commutative algebras ⋮ Poisson traces, D-modules, and symplectic resolutions ⋮ Poisson geometry and representations of PI 4-dimensional Sklyanin algebras ⋮ Cherednik, Hecke and quantum algebras as free Frobenius and Calabi-Yau extensions ⋮ Unruffled extensions and flatness over central subalgebras. ⋮ Harish-Chandra bimodules over rational Cherednik algebras ⋮ Finite-dimensional simple Poisson modules ⋮ PBW-basis for universal enveloping algebras of differential graded Poisson algebras ⋮ Discriminants of Taft algebra smash products and applications ⋮ Realization of Poisson enveloping algebra ⋮ Double affine Hecke algebras at roots of unity ⋮ Le Groupe des Traces de Poisson de Certaines Algèbres D'invariants ⋮ The orbit method for locally nilpotent infinite-dimensional Lie algebras ⋮ Poisson Dixmier-Moeglin equivalence from a topological point of view ⋮ The number of independent traces and supertraces on symplectic reflection algebras ⋮ Ideals generated by traces or by supertraces in the symplectic reflection algebra H1, ν (I2(2m + 1)) ⋮ Hopf algebra actions and rational ideals ⋮ Quiver gauge theories and symplectic singularities ⋮ On isomorphisms of certain functors for Cherednik algebras ⋮ Traces and supertraces on symplectic reflection algebras ⋮ Unnamed Item
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