Timeline for Star product on functions of a Poisson-Lie group
Current License: CC BY-SA 4.0
4 events
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| Aug 11, 2019 at 10:06 | comment | added | Rik Voorhaar | I left this vague, because it is clear there should be some sort of invariance property, but I haven't figured out exactly what it should be. Note that the Poisson structure on a Poisson-Lie group is always zero at the origin (and linear in a neighborhood of the identity). However, the Poisson bivector is still determined by its germ at the identity. I had a similar kind of invariance in mind for the star product. But perhaps one can not extend it beyond a (formal) neighborhood of the identity. | |
| Aug 9, 2019 at 16:17 | comment | added | Heinz Doofenschmirtz | Can you please say what kind of invariance you are talking about? The identification of $U\mathfrak g$ with invariant differential operators uses the left( or right) multiplication, whereas the Kontsevich star product of a Poisson Lie structure is never inariant with respect to the left multiplication unless the Poisson tensor is zero. | |
| Aug 9, 2019 at 10:11 | history | edited | YCor |
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| Aug 9, 2019 at 10:06 | history | asked | Rik Voorhaar | CC BY-SA 4.0 |