ON THE PRIME SPECTRUM OF THE ENVELOPING ALGEBRA AND CHARACTERISTIC VARIETIES

2007 ◽  
Vol 06 (03) ◽  
pp. 369-383 ◽  
Author(s):  
NIKOLAOS PAPALEXIOU
Keyword(s):  
Topological Space ◽  
Lie Algebra ◽  
Prime Ideals ◽  
Prime Spectrum ◽  
Semisimple Lie Algebra ◽  
Characteristic Variety ◽  
Enveloping Algebra ◽  
Commutative Algebras ◽  
Order Relations ◽  
Characteristic Varieties

Let 𝔤 be a semisimple Lie algebra and U(𝔤), its enveloping algebra. A problem in the theory of non-commutative algebras is the description of the set Spec U(𝔤) of prime ideals in U(𝔤) as topological space. Using the notion of the characteristic variety as introduced by Joseph, we compute some order relations between prime ideals.

scholarly journals Chern characters, reduced ranks and -modules on the flag variety

1994 ◽  
Vol 37 (3) ◽  
pp. 477-482 ◽  
Author(s):  
T. J. Hodges ◽  
M. P. Holland
Keyword(s):  
Lie Algebra ◽  
Euler Characteristic ◽  
Maximal Ideal ◽  
Chern Character ◽  
Flag Variety ◽  
Central Character ◽  
Geometric Description ◽  
Semisimple Lie Algebra ◽  
Enveloping Algebra ◽  
Chern Characters

Let D be the factor of the enveloping algebra of a semisimple Lie algebra by its minimal primitive ideal with trival central character. We give a geometric description of the Chern character ch: K0(D)→HC0(D) and the state (of the maximal ideal m) s: K0(D)→K0(D/m) = ℤ in terms of the Euler characteristic χ:K0()→ℤ, where is the associated flag variety.

scholarly journals PRIME SPECTRA OF AMBISKEW POLYNOMIAL RINGS

2018 ◽  
Vol 61 (1) ◽  
pp. 49-68
Author(s):  
CHRISTOPHER D. FISH ◽  
DAVID A. JORDAN
Keyword(s):  
Positive Integer ◽  
Polynomial Algebra ◽  
Central Element ◽  
Universal Enveloping Algebra ◽  
Polynomial Rings ◽  
Prime Ideals ◽  
Closed Field ◽  
Prime Spectrum ◽  
Enveloping Algebra ◽  
Root Of Unity

AbstractWe determine sufficient criteria for the prime spectrum of an ambiskew polynomial algebra R over an algebraically closed field 𝕂 to be akin to those of two of the principal examples of such an algebra, namely the universal enveloping algebra U(sl2) (in characteristic 0) and its quantization Uq(sl2) (when q is not a root of unity). More precisely, we determine sufficient criteria for the prime spectrum of R to consist of 0, the ideals (z − λ)R for some central element z of R and all λ ∈ 𝕂, and, for some positive integer d and each positive integer m, d height two prime ideals P for which R/P has Goldie rank m.

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