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Abstract
Let $W_+$ be the {\em positive Witt algebra}, which has a $\CC$basis $\{e_n: n \in \ZZ_{\geq 1}\}$, with Lie bracket $[ e_i, e_j] = (ji) e_{i+j}$.
We study the twosided ideal structure of the universal enveloping algebra $\U(W_+)$ of $W_+$.
We show that if $I$ is a (twosided) ideal of $\U(W_+)$ generated by quadratic expressions in the $e_i$, then $\U(W_+)/I$ has finite GelfandKirillov dimension, and that such ideals satisfy the ascending chain condition.
We conjecture that analogous facts hold for arbitrary ideals of $\U(W_+)$, and verify a version of these conjectures for radical Poisson ideals of the symmetric algebra ${\rm S}(W_+)$.
We study the twosided ideal structure of the universal enveloping algebra $\U(W_+)$ of $W_+$.
We show that if $I$ is a (twosided) ideal of $\U(W_+)$ generated by quadratic expressions in the $e_i$, then $\U(W_+)/I$ has finite GelfandKirillov dimension, and that such ideals satisfy the ascending chain condition.
We conjecture that analogous facts hold for arbitrary ideals of $\U(W_+)$, and verify a version of these conjectures for radical Poisson ideals of the symmetric algebra ${\rm S}(W_+)$.
Original language  English 

Pages (fromto)  15691599 
Number of pages  31 
Journal  Algebras and representation theory 
Volume  23 
Early online date  14 Jun 2019 
DOIs  
Publication status  Published  31 Aug 2020 
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Dive into the research topics of 'Ideals in the enveloping algebra of the positive Witt algebra'. Together they form a unique fingerprint.Projects
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Sue Sierra
 School of Mathematics  Personal Chair of Noncommutative Algebra
Person: Academic: Research Active