Questions tagged [primitive-ideal]
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7 questions
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Two-sided cells, special nilpotent orbits and special representations
Let $\mathfrak{g}$ be a complex semisimple Lie algebra. This question concerns three classical objects of representation theory: the two-sided Kazhdan-Lusztig cells of the Weyl group $W$ of $\mathfrak{...
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Explicit example of prime ideal not an intersection of maximal ideals, in universal enveloping algebra
Let $A$ be a $\mathbb k$-algebra. If $A$ is affine commutative, by Nullstellensatz, then every prime ideal of $A$ is an intersection of maximal ideals.
To justify the notion of being primitive in ...
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Nontrivial primitivity of full matrix ring
Let $V$ be an infinite dimensional vector space, $A$ its algebra of linear endomorphisms (also known as a full matrix ring). The algebra $A$ is primitive because $V$ is a faithful simple (left) $A$-...
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Ideals of affine space curves
Given some algebraic closed curve in the affine space $\mathbb{A}^3_\mathbb{C}$, is there a way to decide whether its ideal (polynomials in $\mathbb{C}[X,Y,Z]$ vanishing on the curve) is generated by ...
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Reference on ideal theory in Hurwitz quaternions
I am looking for a book that studies the set of Hurwitz quaternions (HQ). In particular, I am interested in a connection between HQ and imaginary quadratic fields (IQF); quaternion orders $\mathcal{O}(...
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Status of Borho and Brylinski's irreducibility conjectures?
In Differential Operators on Homogeneous Spaces, III, Section 6.7, Borho and Brylinski make a long series of equivalent conjectures which they show are all equivalent. Perhaps the easiest statement ...
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What are the "special" strata of Sym^n(C^2)?
The affine variety $Sym^n(\mathbb{C}^2)$ has a natural quantization as a spherical rational Cherednik algebra. Thus, any primitive ideal of the rational Cherednik algebra has an corresponding ideal ...
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