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Noncommutative differential geometry, and the matrix representations of generalised algebras

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Noncommutative differential geometry, and the matrix representations of generalised algebras. / Gratus, Jonathan.
In: Journal of Geometry and Physics, Vol. 25, No. 3-4, 05.1998, p. 227-244.

Research output: Contribution to Journal/Magazine › Journal article › peer-review

Harvard

Gratus, J 1998, 'Noncommutative differential geometry, and the matrix representations of generalised algebras', Journal of Geometry and Physics, vol. 25, no. 3-4, pp. 227-244. https://doi.org/10.1016/S0393-0440(97)00027-2

APA

Gratus, J. (1998). Noncommutative differential geometry, and the matrix representations of generalised algebras. Journal of Geometry and Physics, 25(3-4), 227-244. https://doi.org/10.1016/S0393-0440(97)00027-2

Vancouver

Gratus J. Noncommutative differential geometry, and the matrix representations of generalised algebras. Journal of Geometry and Physics. 1998 May;25(3-4):227-244. doi: 10.1016/S0393-0440(97)00027-2

Author

Gratus, Jonathan. / Noncommutative differential geometry, and the matrix representations of generalised algebras. In: Journal of Geometry and Physics. 1998 ; Vol. 25, No. 3-4. pp. 227-244.

Bibtex

@article{ff569e7e3af6428d928662fbddec37c8,
title = "Noncommutative differential geometry, and the matrix representations of generalised algebras",
abstract = "The underlying algebra for a noncommutative geometry is taken to be a matrix algebra, and the set of derivatives the adjoint of a subset of traceless matrices. This is sufficient to calculate the dual I-forms, and show that the space of 1-forms is a free module over the algebra of matrices. The concept of a generalised algebra is defined and it is shown that this is required in order for the space of 2-forms to exist. The exterior derivative is generalised for higher-order forms and these ale also shown to be: free modules over the matrix algebra. Examples of mappings that preserve the differential structure are given. Also given are four examples of matrix generalised algebras. and the corresponding noncommutative geometries. including the cases where the generalised algebra corresponds to a representation of a Lie algebra or a q-deformed algebra.",
keywords = "generalised algebra, noncommutative geometry, LINEAR CONNECTIONS",
author = "Jonathan Gratus",
year = "1998",
month = may,
doi = "10.1016/S0393-0440(97)00027-2",
language = "English",
volume = "25",
pages = "227--244",
journal = "Journal of Geometry and Physics",
issn = "0393-0440",
publisher = "Elsevier",
number = "3-4",

}

RIS

TY - JOUR

T1 - Noncommutative differential geometry, and the matrix representations of generalised algebras

AU - Gratus, Jonathan

PY - 1998/5

Y1 - 1998/5

N2 - The underlying algebra for a noncommutative geometry is taken to be a matrix algebra, and the set of derivatives the adjoint of a subset of traceless matrices. This is sufficient to calculate the dual I-forms, and show that the space of 1-forms is a free module over the algebra of matrices. The concept of a generalised algebra is defined and it is shown that this is required in order for the space of 2-forms to exist. The exterior derivative is generalised for higher-order forms and these ale also shown to be: free modules over the matrix algebra. Examples of mappings that preserve the differential structure are given. Also given are four examples of matrix generalised algebras. and the corresponding noncommutative geometries. including the cases where the generalised algebra corresponds to a representation of a Lie algebra or a q-deformed algebra.

AB - The underlying algebra for a noncommutative geometry is taken to be a matrix algebra, and the set of derivatives the adjoint of a subset of traceless matrices. This is sufficient to calculate the dual I-forms, and show that the space of 1-forms is a free module over the algebra of matrices. The concept of a generalised algebra is defined and it is shown that this is required in order for the space of 2-forms to exist. The exterior derivative is generalised for higher-order forms and these ale also shown to be: free modules over the matrix algebra. Examples of mappings that preserve the differential structure are given. Also given are four examples of matrix generalised algebras. and the corresponding noncommutative geometries. including the cases where the generalised algebra corresponds to a representation of a Lie algebra or a q-deformed algebra.

KW - generalised algebra

KW - noncommutative geometry

KW - LINEAR CONNECTIONS

U2 - 10.1016/S0393-0440(97)00027-2

DO - 10.1016/S0393-0440(97)00027-2

M3 - Journal article

VL - 25

SP - 227

EP - 244

JO - Journal of Geometry and Physics

JF - Journal of Geometry and Physics

SN - 0393-0440

IS - 3-4

ER -