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Abstract
Let g be the Witt algebra or the positive Witt algebra. It is well known that the enveloping algebra U(g) has intermediate growth and thus infinite Gelfand–Kirillov (GK) dimension. We prove that the GKdimension of U(g) is just infinite in the sense that any proper quotient of U(g) has polynomial growth. This proves a conjecture of Petukhov and the second named author for the positive Witt algebra. We also establish the corresponding results for quotients of the symmetric algebra S(g) by proper Poisson ideals.
In fact, we prove more generally that any central quotient of the universal enveloping algebra of the Virasoro algebra has just infinite GKdimension. We give several applications. In particular, we easily compute the annihilators of Verma modules over the Virasoro algebra.
In fact, we prove more generally that any central quotient of the universal enveloping algebra of the Virasoro algebra has just infinite GKdimension. We give several applications. In particular, we easily compute the annihilators of Verma modules over the Virasoro algebra.
Original language  English 

Pages (fromto)  285306 
Journal  Arkiv for Matematik 
Volume  58 
Issue number  2 
DOIs  
Publication status  Published  31 Oct 2020 
Keywords
 math.RA
 mathph
 math.AG
 math.MP
 math.QA
 math.RT
 16S30, 17B68, 16P90, 17B65
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Sue Sierra
 School of Mathematics  Personal Chair of Noncommutative Algebra
Person: Academic: Research Active