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Dippell, Marvin; Esposito, Chiara; Waldmann, Stefan

doi:10.25537/dm.2019v24.1811-1853

Cited by 4 publications

(3 citation statements)

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“…10 We thus have an exact sequence (1) of Poisson algebra maps, where the quotient algebra B is interpreted as algebra of smooth functions on what we would call geometrically the reduced phase space M red . 11 "Good" star products on M induce formal deformations of the constrained ideal, normalizer and reduced phase space, fitting an exact sequence:…”

Section: Deformation Of Poisson Submanifolds Supposementioning

confidence: 99%

“…For a general discussion of the problem one can see the review [6] and references therein. A more recent "categorical" approach is in [11].…”

Section: Deformation Of Poisson Submanifolds Supposementioning

confidence: 99%

“…The normalizer is indeed the largest Poisson subalgebra of C ∞ (M), { , } containing J as a Lie ideal 11. Note that if S is a symplectic submanifold, then A = C ∞ (M) and M red ≃ S.…”

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confidence: 99%

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On the Notion of Noncommutative Submanifold

D'Andrea

2019

Preprint

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We review the notion of submanifold algebra, as introduced by T. Masson, and discuss some properties and examples. A submanifold algebra of an associative algebra A is a quotient algebra B such that all derivations of B can be lifted to A. We will argue that in the case of smooth functions on manifolds every quotient algebra is a submanifold algebra, derive a topological obstruction when the algebras are deformation quantizations of symplectic manifolds, present some (commutative and noncommutative) examples and counterexamples.

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Section: Deformation Of Poisson Submanifolds Supposementioning

confidence: 99%

“…For a general discussion of the problem one can see the review [6] and references therein. A more recent "categorical" approach is in [11].…”

Section: Deformation Of Poisson Submanifolds Supposementioning

confidence: 99%