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On the local structure of quantizations in characteristic p
Author(s) -
Tikaradze Akaki
Publication year - 2018
Publication title -
bulletin of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 2.396
H-Index - 48
eISSN - 1469-2120
pISSN - 0024-6093
DOI - 10.1112/blms.12128
Subject(s) - mathematics , tensor product , poisson distribution , pure mathematics , affine transformation , weyl algebra , algebra over a field , variety (cybernetics) , quantization (signal processing) , statistics , algorithm
Let A be a central quantization of an affine Poisson variety X over a field of characteristic p > 0 . We show that the completion of A with repect to a closed point y ∈ X is isomorphic to the tensor product of the Weyl algebra with a local Poisson algebra. This result can be thought of as a positive characteristic analogue of results of Losev and Kaledin about slice algebras of quantizations in characteristic 0.