On the Maximal Primitive Ideal Corresponding to the Model Nilpotent Orbit

2012 ◽  
Vol 2012 (24) ◽  
pp. 5731-5743 ◽  
Author(s):  
Hung Yean Loke ◽  
Gordan Savin
Keyword(s):  
Nilpotent Orbit ◽  
Primitive Ideal

scholarly journals Some groups with T1 primitive ideal spaces

1985 ◽  
Vol 38 (1) ◽  
pp. 55-64 ◽  
Author(s):  
A. L. Carey ◽  
W. Moran
Keyword(s):  
Normal Subgroup ◽  
Lie Groups ◽  
Lie Group ◽  
Locally Compact Group ◽  
Primitive Ideal ◽  
Ideal Space ◽  
Solvable Lie Groups ◽  
Locally Compact ◽  
Simply Connected ◽  
Connected Lie Group

AbstractLet G be a second countable locally compact group possessing a normal subgroup N with G/N abelian. We prove that if G/N is discrete then G has T1 primitive ideal space if and only if the G-quasiorbits in Prim N are closed. This condition on G-quasiorbits arose in Pukanzky's work on connected and simply connected solvable Lie groups where it is equivalent to the condition of Auslander and Moore that G be type R on N (-nilradical). Using an abstract version of Pukanzky's arguments due to Green and Pedersen we establish that if G is a connected and simply connected Lie group then Prim G is T1 whenever G-quasiorbits in [G, G] are closed.

scholarly journals W algebras, cosets and VOAs for 4d $$ \mathcal{N} $$ = 2 SCFTs from M5 branes

2021 ◽  
Vol 2021 (4) ◽  
Author(s):  
Dan Xie ◽  
Wenbin Yan
Keyword(s):  
Vertex Operator ◽  
Operator Algebras ◽  
Nilpotent Orbit ◽  
Vertex Operator Algebras ◽  
Flavor Symmetries ◽  
Conformal Embedding

Abstract We identify vertex operator algebras (VOAs) of a class of Argyres-Douglas (AD) matters with two types of non-abelian flavor symmetries. They are the W algebras defined using nilpotent orbit with partition [qm, 1s]. Gauging above AD matters, we can find VOAs for more general $$ \mathcal{N} $$ N = 2 SCFTs engineered from 6d (2, 0) theories. For example, the VOA for general (AN − 1, Ak − 1) theory is found as the coset of a collection of above W algebras. Various new interesting properties of 2d VOAs such as level-rank duality, conformal embedding, collapsing levels, coset constructions for known VOAs can be derived from 4d theory.

scholarly journals WREATH PRODUCTS, NILPOTENT ORBITS AND SYMPLECTIC DEFORMATIONS

2007 ◽  
Vol 18 (05) ◽  
pp. 473-481
Author(s):  
BAOHUA FU
Keyword(s):  
Wreath Product ◽  
Wreath Products ◽  
Nilpotent Orbit ◽  
Nilpotent Orbits ◽  
Symplectic Resolutions

We recover the wreath product X ≔ Sym 2(ℂ2/± 1) as a transversal slice to a nilpotent orbit in 𝔰𝔭6. By using deformations of Springer resolutions, we construct a symplectic deformation of symplectic resolutions of X.

scholarly journals Reduction of filtered K-theory and a characterization of Cuntz-Krieger algebras

2014 ◽  
Vol 14 (3) ◽  
pp. 570-613 ◽  
Author(s):  
Sara E. Arklint ◽  
Rasmus Bentmann ◽  
Takeshi Katsura
Keyword(s):  
Primitive Ideal ◽  
Ideal Space ◽  
Real Rank ◽  
Real Rank Zero ◽  
Rank Zero ◽  
K Theory

AbstractWe show that filtered K-theory is equivalent to a substantially smaller invariant for all real-rank-zero C*-algebras with certain primitive ideal spaces—including the infinitely many so-called accordion spaces for which filtered K-theory is known to be a complete invariant. As a consequence, we give a characterization of purely infinite Cuntz–Krieger algebras whose primitive ideal space is an accordion space.

The Primitive Ideal Type of Reality

2005 ◽  
pp. 71-124
Author(s):  
Mónica Judith Sánchez Flores
Keyword(s):  
Ideal Type ◽  
Primitive Ideal

scholarly journals Tangent loci and certain linear sections of adjoint varieties

2000 ◽  
Vol 158 ◽  
pp. 63-72
Author(s):  
Hajime Kaji ◽  
Osami Yasukura
Keyword(s):  
Lie Algebra ◽  
Projective Variety ◽  
Linear Subspace ◽  
Nilpotent Orbit ◽  
Contact Type ◽  
Simple Lie Algebra ◽  
Veronese Variety ◽  
Linear Sections

AbstractAn adjoint variety X(g)associated to a complex simple Lie algebra is by definition a projective variety in ℙ*(g) obtained as the projectivization of the (unique) non-zero, minimal nilpotent orbit in g. We first describe the tangent loci of X(g) in terms of triples. Secondly for a graded decomposition of contact type we show that the intersection of X(g) and the linear subspace ℙ*(g1) in ℙ*(g) coincides with the cubic Veronese variety associated to g.

scholarly journals On the minimal modules for exceptional Lie algebras: Jordan blocks and stabilizers

2016 ◽  
Vol 19 (1) ◽  
pp. 235-258 ◽  
Author(s):  
David I. Stewart
Keyword(s):  
Algebraic Group ◽  
Lie Algebras ◽  
Nilpotent Orbit ◽  
Closed Field ◽  
Algebraically Closed Field ◽  
Exceptional Lie Algebras ◽  
Induced Module ◽  
Simply Connected

Let $G$ be a simple simply connected exceptional algebraic group of type $G_{2}$, $F_{4}$, $E_{6}$ or $E_{7}$ over an algebraically closed field $k$ of characteristic $p>0$ with $\mathfrak{g}=\text{Lie}(G)$. For each nilpotent orbit $G\cdot e$ of $\mathfrak{g}$, we list the Jordan blocks of the action of $e$ on the minimal induced module $V_{\text{min}}$ of $\mathfrak{g}$. We also establish when the centralizers $G_{v}$ of vectors $v\in V_{\text{min}}$ and stabilizers $\text{Stab}_{G}\langle v\rangle$ of $1$-spaces $\langle v\rangle \subset V_{\text{min}}$ are smooth; that is, when $\dim G_{v}=\dim \mathfrak{g}_{v}$ or $\dim \text{Stab}_{G}\langle v\rangle =\dim \text{Stab}_{\mathfrak{g}}\langle v\rangle$.

scholarly journals JOSEPH IDEALS AND LISSE MINIMAL -ALGEBRAS

2016 ◽  
Vol 17 (2) ◽  
pp. 397-417 ◽  
Author(s):  
Tomoyuki Arakawa ◽  
Anne Moreau
Keyword(s):  
Nilpotent Orbit ◽  
Vertex Algebras ◽  
Orbit Closure ◽  
New Family ◽  
Orbit Closures

We consider a lifting of Joseph ideals for the minimal nilpotent orbit closure to the setting of affine Kac–Moody algebras and find new examples of affine vertex algebras whose associated varieties are minimal nilpotent orbit closures. As an application we obtain a new family of lisse ($C_{2}$-cofinite)$W$-algebras that are not coming from admissible representations of affine Kac–Moody algebras.

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