The Chern character for Lie-Rinehart algebras

Helge Maakestad[1]

  • [1] Université Paris VII, Institut de Mathématiques, case 247, 4 place Jussieu, 75252 Paris Cedex (France)

Annales de l'institut Fourier (2005)

  • Volume: 55, Issue: 7, page 2551-2574
  • ISSN: 0373-0956

Abstract

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Let A be a commutative S -algebra where S is a ring containing the rationals. We prove the existence of a Chern character for Lie-Rinehart algebras L over A with values in the Lie-Rinehart cohomology of L which is independent of choice of a L -connection. Our result generalizes the classical Chern character from the K -theory of A to the algebraic De Rham cohomology.

How to cite

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Maakestad, Helge. "The Chern character for Lie-Rinehart algebras." Annales de l'institut Fourier 55.7 (2005): 2551-2574. <http://eudml.org/doc/116263>.

@article{Maakestad2005,
abstract = {Let $A$ be a commutative $S$-algebra where $S$ is a ring containing the rationals. We prove the existence of a Chern character for Lie-Rinehart algebras $L$ over A with values in the Lie-Rinehart cohomology of L which is independent of choice of a $L$-connection. Our result generalizes the classical Chern character from the $K$-theory of $A$ to the algebraic De Rham cohomology.},
affiliation = {Université Paris VII, Institut de Mathématiques, case 247, 4 place Jussieu, 75252 Paris Cedex (France)},
author = {Maakestad, Helge},
journal = {Annales de l'institut Fourier},
keywords = {Lie-Rinehart algebra; connection; de Rham cohomology; Lie-Rinehart cohomology; Jacobsons Galois correspondence},
language = {eng},
number = {7},
pages = {2551-2574},
publisher = {Association des Annales de l'Institut Fourier},
title = {The Chern character for Lie-Rinehart algebras},
url = {http://eudml.org/doc/116263},
volume = {55},
year = {2005},
}

TY - JOUR
AU - Maakestad, Helge
TI - The Chern character for Lie-Rinehart algebras
JO - Annales de l'institut Fourier
PY - 2005
PB - Association des Annales de l'Institut Fourier
VL - 55
IS - 7
SP - 2551
EP - 2574
AB - Let $A$ be a commutative $S$-algebra where $S$ is a ring containing the rationals. We prove the existence of a Chern character for Lie-Rinehart algebras $L$ over A with values in the Lie-Rinehart cohomology of L which is independent of choice of a $L$-connection. Our result generalizes the classical Chern character from the $K$-theory of $A$ to the algebraic De Rham cohomology.
LA - eng
KW - Lie-Rinehart algebra; connection; de Rham cohomology; Lie-Rinehart cohomology; Jacobsons Galois correspondence
UR - http://eudml.org/doc/116263
ER -

References

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  8. J. Kubarski, Tangential Chern-Weil homomorphism, Geometric study of foliations, World. Sci. Publishing (1994) MR1363733
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  13. C. Weibel, An introduction to homological algebra, 38 (1994), Cambridge University Press Zbl0797.18001MR1269324

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