Journal
ALGEBRAS AND REPRESENTATION THEORY
Volume 23, Issue 4, Pages 1569-1599Publisher
SPRINGER
DOI: 10.1007/s10468-019-09896-2
Keywords
Witt algebra; Positive Witt algebra; Poisson algebra; Poisson Gelfand-Kirillov dimension; Ascending chain condition; Primary
Categories
Funding
- Leverhulme Trust [RPG-2013-293]
- RFBR [16-01-00818]
- EPSRC [EP/M008460/1]
- EPSRC [EP/M008460/1] Funding Source: UKRI
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Let W+ be thepositive Witt algebra, which has a C-basis {e(n): n is an element of Z >= 1}, with Lie bracket [e(i),e(j)] = (j-i)e(i+j). We study the two-sided ideal structure of the universal enveloping algebra U(W+) ofW(+). We show that ifIis a (two-sided) ideal of U(W+) generated by quadratic expressions in thee(i), then U(W+)/Ihas finite Gelfand-Kirillov 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 S(W+).
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