Definitions for supergeometry
su·per·ge·om·e·t·ry

WiktionaryRate this definition:0.0 / 0 votes

1. supergeometrynoun

   A differential geometry of modules over graded commutative algebras, supermanifolds and graded manifolds

WikipediaRate this definition:0.0 / 0 votes

1. Supergeometry

   Supergeometry is differential geometry of modules over graded commutative algebras, supermanifolds and graded manifolds. Supergeometry is part and parcel of many classical and quantum field theories involving odd fields, e.g., SUSY field theory, BRST theory, or supergravity. Supergeometry is formulated in terms of Z 2 {\displaystyle \mathbb {Z} _{2}} -graded modules and sheaves over Z 2 {\displaystyle \mathbb {Z} _{2}} -graded commutative algebras (supercommutative algebras). In particular, superconnections are defined as Koszul connections on these modules and sheaves. However, supergeometry is not particular noncommutative geometry because of a different definition of a graded derivation. Graded manifolds and supermanifolds also are phrased in terms of sheaves of graded commutative algebras. Graded manifolds are characterized by sheaves on smooth manifolds, while supermanifolds are constructed by gluing of sheaves of supervector spaces. There are different types of supermanifolds. These are smooth supermanifolds ( H ∞ {\displaystyle H^{\infty }} -, G ∞ {\displaystyle G^{\infty }} -, G H ∞ {\displaystyle GH^{\infty }} -supermanifolds), G {\displaystyle G} -supermanifolds, and DeWitt supermanifolds. In particular, supervector bundles and principal superbundles are considered in the category of G {\displaystyle G} -supermanifolds. Definitions of principal superbundles and principal superconnections straightforwardly follow that of smooth principal bundles and principal connections. Principal graded bundles also are considered in the category of graded manifolds. There is a different class of Quillen–Ne'eman superbundles and superconnections. These superconnections have been applied to computing the Chern character in K-theory, noncommutative geometry, and BRST formalism.

WikidataRate this definition:0.0 / 0 votes

1. Supergeometry

   Supergeometry is differential geometry of modules over graded commutative algebras, supermanifolds and graded manifolds. Supergeometry is part and parcel of many classical and quantum field theories involving odd fields, e.g., SUSY field theory, BRST theory, or supergravity. Supergeometry is formulated in terms of -graded modules and sheaves over -graded commutative algebras. In particular, superconnections are defined as Koszul connections on these modules and sheaves. However, supergeometry is not particular noncommutative geometry because of a different definition of a graded derivation. Graded manifolds and supermanifolds also are phrased in terms of sheaves of graded commutative algebras. Graded manifolds are characterized by sheaves on smooth manifolds, while supermanifolds are constructed by gluing of sheaves of supervector spaces. Note that there are different types of supermanifolds. These are smooth supermanifolds, -supermanifolds, and DeWitt supermanifolds. In particular, supervector bundles and principal superbundles are considered in the category of -supermanifolds. Note that definitions of principal superbundles and principal superconnections straightforwardly follow that of smooth principal bundles and principal connections. Principal graded bundles also are considered in the category of graded manifolds.

How to pronounce supergeometry?

1. Alex

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   David

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   Mark

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   Daniel

   British

   Libby

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   Mia

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   Australian

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   Australian

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   Oliver

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   South African

How to say supergeometry in sign language?

Numerology

1. Chaldean Numerology

   The numerical value of supergeometry in Chaldean Numerology is: 1

2. Pythagorean Numerology

   The numerical value of supergeometry in Pythagorean Numerology is: 7

References

1. ^ Wiktionary
   https://en.wiktionary.org/wiki/Supergeometry
2. ^ Wikipedia
   https://en.wikipedia.org/wiki/Supergeometry
3. ^ Wikidata
   https://www.wikidata.org/w/index.php?search=supergeometry