Noncommutative Deformations of Locally Symmetric K\"ahler manifolds

Akifumi Sako; Kentaro Hara

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Noncommutative Deformations of Locally Symmetric K\"ahler manifolds

Kentaro Hara, Akifumi Sako

Mathematical Physics · Submitted 29 Aug 2016

abstract compiled · 2026-09-23 · no language-model review

The authors' main claim We derive algebraic recurrence relations to obtain a deformation quantization with separation of variables for a locally symmetric K\"ahler manifold.

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Compiled by classifier-1.13.0 via TypeSafe API, question bank abstract-p1-20260923, 2026-09-23: 1 request, 3,592 input tokens.

What the abstract itself states, as probabilities: claims first 0.03 · states limitation 0.07 · human participants 0.01 · controlled comparison 0.01 · randomized assignment 0.01 · states quantitative result 0.05 · compares with prior results 0.35 · mentions code or data availability 0.02.

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We derive algebraic recurrence relations to obtain a deformation quantization with separation of variables for a locally symmetric K\"ahler manifold. This quantization method is one of the ways to perform a deformation quantization of K\"ahler manifolds, which is introduced by Karabegov. From the recurrence relations, concrete expressions of star products for one-dimensional local symmetric K\"ahler manifolds and ${\mathbb C}P^N$ are constructed. The recurrence relations for a Grassmann manifold $G_{2,2}$ are closely studied too.

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#	sentence	role	the authors' own work	states the main conclusion	strength
s0	We derive algebraic recurrence relations to obtain a deformation quantization with separation of variables for a locally symmetric K\"ahler manifold.	contribution 0.80	0.96	0.73	asserted 1.00
s1	This quantization method is one of the ways to perform a deformation quantization of K\"ahler manifolds, which is introduced by Karabegov.	background 0.98	0.06	0.07	asserted 0.99
s2	From the recurrence relations, concrete expressions of star products for one-dimensional local symmetric K\"ahler manifolds and ${\mathbb C}P^N$ are constructed.	result 0.85	0.93	0.31	asserted 1.00
s3	The recurrence relations for a Grassmann manifold $G_{2,2}$ are closely studied too.	contribution 0.95	0.88	0.06	asserted 1.00

What kind of paper the classifier reports this is: theoretical result 0.69 · evidence from proof or derivation 1.00.

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The paper

Original abstract

We derive algebraic recurrence relations to obtain a deformation quantization with separation of variables for a locally symmetric K\"ahler manifold. This quantization method is one of the ways to perform a deformation quantization of K\"ahler manifolds, which is introduced by Karabegov. From the recurrence relations, concrete expressions of star products for one-dimensional local symmetric K\"ahler manifolds and ${\mathbb C}P^N$ are constructed. The recurrence relations for a Grassmann manifold $G_{2,2}$ are closely studied too.

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1 arXiv paper cite this in 18 sentences

Each citing sentence is taken from the citing paper's LaTeX source and typed by Pith's classifier. A label appears at probability 0.8 or more (0.95 for support), a contest at 0.7 or more; the quoted words are the citing authors'. How each label was checked · JSON

Papers citing it · 13 sentences without a confident label

Uses its method or tool 1 paper

In order to give an explicit star product with separation of variables on $G_2,4(ℂ)$ by using the construction method proposed by [ref] , it is necessary to solve the recurrence relations.

Deformation Quantization with Separation of Variables of $G_{2,4}(\mathbb{C})$ · Introduction · 0.97

Cites it as background 1 paper

[ref] related to a deformation quantization with separation of variables for a locally symmetric Kähler manifold.

Deformation Quantization with Separation of Variables of $G_{2,4}(\mathbb{C})$ · Introduction · 0.88

What it cites · 10 sentences without a confident label

Contests 1 paper

The method in this article overcome the problems in [ref] .

Explicit Formulae for Noncommutative Deformations of CP^N and CH^N · Introduction · contest 0.73

Compares with 1 paper

As an example, we constructed a star product for $ℂP^N$, that is equal to the star product in [ref] , but it has a different expression.

Explicit Formulae for Noncommutative Deformations of CP^N and CH^N · Conclusion · 1.00

Cites as background 2 papers

After [ref] , several ways of deformation quantization were proposed [ref] .

Deformation quantization of Poisson manifolds, I · Introduction · 0.98
In [ref] , the Fock representation for noncommutative $ℂP^N$ is constructed.

Gauge theories on noncommutative ${\mathbb C}P^N$ and BPS-like equations · Conclusion · 0.80

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