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• W2000546535 abstract "With a nilpotent element in a semisimple Lie algebra <inline-formula content-type=math/mathml> <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML alttext=German g> <mml:semantics> <mml:mrow class=MJX-TeXAtom-ORD> <mml:mi mathvariant=fraktur>g</mml:mi> </mml:mrow> <mml:annotation encoding=application/x-tex>mathfrak {g}</mml:annotation> </mml:semantics> </mml:math> </inline-formula> one associates a finitely generated associative algebra <inline-formula content-type=math/mathml> <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML alttext=script upper W> <mml:semantics> <mml:mrow class=MJX-TeXAtom-ORD> <mml:mi class=MJX-tex-caligraphic mathvariant=script>W</mml:mi> </mml:mrow> <mml:annotation encoding=application/x-tex>mathcal {W}</mml:annotation> </mml:semantics> </mml:math> </inline-formula> called <italic>a <inline-formula content-type=math/mathml> <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML alttext=upper W> <mml:semantics> <mml:mi>W</mml:mi> <mml:annotation encoding=application/x-tex>W</mml:annotation> </mml:semantics> </mml:math> </inline-formula>-algebra of finite type</italic>. This algebra is obtained from the universal enveloping algebra <inline-formula content-type=math/mathml> <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML alttext=upper U left-parenthesis German g right-parenthesis> <mml:semantics> <mml:mrow> <mml:mi>U</mml:mi> <mml:mo stretchy=false>(</mml:mo> <mml:mrow class=MJX-TeXAtom-ORD> <mml:mi mathvariant=fraktur>g</mml:mi> </mml:mrow> <mml:mo stretchy=false>)</mml:mo> </mml:mrow> <mml:annotation encoding=application/x-tex>U(mathfrak {g})</mml:annotation> </mml:semantics> </mml:math> </inline-formula> by a certain Hamiltonian reduction. We observe that <inline-formula content-type=math/mathml> <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML alttext=script upper W> <mml:semantics> <mml:mrow class=MJX-TeXAtom-ORD> <mml:mi class=MJX-tex-caligraphic mathvariant=script>W</mml:mi> </mml:mrow> <mml:annotation encoding=application/x-tex>mathcal {W}</mml:annotation> </mml:semantics> </mml:math> </inline-formula> is the invariant algebra for an action of a reductive group <inline-formula content-type=math/mathml> <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML alttext=upper G> <mml:semantics> <mml:mi>G</mml:mi> <mml:annotation encoding=application/x-tex>G</mml:annotation> </mml:semantics> </mml:math> </inline-formula> with Lie algebra <inline-formula content-type=math/mathml> <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML alttext=German g> <mml:semantics> <mml:mrow class=MJX-TeXAtom-ORD> <mml:mi mathvariant=fraktur>g</mml:mi> </mml:mrow> <mml:annotation encoding=application/x-tex>mathfrak {g}</mml:annotation> </mml:semantics> </mml:math> </inline-formula> on a quantized symplectic affine variety and use this observation to study <inline-formula content-type=math/mathml> <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML alttext=script upper W> <mml:semantics> <mml:mrow class=MJX-TeXAtom-ORD> <mml:mi class=MJX-tex-caligraphic mathvariant=script>W</mml:mi> </mml:mrow> <mml:annotation encoding=application/x-tex>mathcal {W}</mml:annotation> </mml:semantics> </mml:math> </inline-formula>. Our results include an alternative definition of <inline-formula content-type=math/mathml> <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML alttext=script upper W> <mml:semantics> <mml:mrow class=MJX-TeXAtom-ORD> <mml:mi class=MJX-tex-caligraphic mathvariant=script>W</mml:mi> </mml:mrow> <mml:annotation encoding=application/x-tex>mathcal {W}</mml:annotation> </mml:semantics> </mml:math> </inline-formula>, a relation between the sets of prime ideals of <inline-formula content-type=math/mathml> <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML alttext=script upper W> <mml:semantics> <mml:mrow class=MJX-TeXAtom-ORD> <mml:mi class=MJX-tex-caligraphic mathvariant=script>W</mml:mi> </mml:mrow> <mml:annotation encoding=application/x-tex>mathcal {W}</mml:annotation> </mml:semantics> </mml:math> </inline-formula> and of the corresponding universal enveloping algebra, the existence of a one-dimensional representation of <inline-formula content-type=math/mathml> <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML alttext=script upper W> <mml:semantics> <mml:mrow class=MJX-TeXAtom-ORD> <mml:mi class=MJX-tex-caligraphic mathvariant=script>W</mml:mi> </mml:mrow> <mml:annotation encoding=application/x-tex>mathcal {W}</mml:annotation> </mml:semantics> </mml:math> </inline-formula> in the case of classical <inline-formula content-type=math/mathml> <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML alttext=German g> <mml:semantics> <mml:mrow class=MJX-TeXAtom-ORD> <mml:mi mathvariant=fraktur>g</mml:mi> </mml:mrow> <mml:annotation encoding=application/x-tex>mathfrak {g}</mml:annotation> </mml:semantics> </mml:math> </inline-formula> and the separation of elements of <inline-formula content-type=math/mathml> <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML alttext=script upper W> <mml:semantics> <mml:mrow class=MJX-TeXAtom-ORD> <mml:mi class=MJX-tex-caligraphic mathvariant=script>W</mml:mi> </mml:mrow> <mml:annotation encoding=application/x-tex>mathcal {W}</mml:annotation> </mml:semantics> </mml:math> </inline-formula> by finite-dimensional representations." @default.
• W2000546535 created "2016-06-24" @default.
• W2000546535 creator A5060786290 @default.
• W2000546535 date "2009-09-18" @default.
• W2000546535 modified "2023-09-30" @default.
• W2000546535 title "Quantized symplectic actions and 𝑊-algebras" @default.
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