On the index of nonlocal elliptic operators for compact Lie groups

Anton Savin

Open Mathematics (2011)

  • Volume: 9, Issue: 4, page 833-850
  • ISSN: 2391-5455

Abstract

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We consider a class of nonlocal operators associated with a compact Lie group G acting on a smooth manifold. A notion of symbol of such operators is introduced and an index formula for elliptic elements is obtained. The symbol in this situation is an element of a noncommutative algebra (crossed product by G) and to obtain an index formula, we define the Chern character for this algebra in the framework of noncommutative geometry.

How to cite

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Anton Savin. "On the index of nonlocal elliptic operators for compact Lie groups." Open Mathematics 9.4 (2011): 833-850. <http://eudml.org/doc/269233>.

@article{AntonSavin2011,
abstract = {We consider a class of nonlocal operators associated with a compact Lie group G acting on a smooth manifold. A notion of symbol of such operators is introduced and an index formula for elliptic elements is obtained. The symbol in this situation is an element of a noncommutative algebra (crossed product by G) and to obtain an index formula, we define the Chern character for this algebra in the framework of noncommutative geometry.},
author = {Anton Savin},
journal = {Open Mathematics},
keywords = {Nonlocal operator; Basic cohomology; Crossed product; Transverse ellipticity; Chern character; Index formula; nonlocal operator; basic cohomology; crossed product; transverse ellipticity; index formula; Fredholm index},
language = {eng},
number = {4},
pages = {833-850},
title = {On the index of nonlocal elliptic operators for compact Lie groups},
url = {http://eudml.org/doc/269233},
volume = {9},
year = {2011},
}

TY - JOUR
AU - Anton Savin
TI - On the index of nonlocal elliptic operators for compact Lie groups
JO - Open Mathematics
PY - 2011
VL - 9
IS - 4
SP - 833
EP - 850
AB - We consider a class of nonlocal operators associated with a compact Lie group G acting on a smooth manifold. A notion of symbol of such operators is introduced and an index formula for elliptic elements is obtained. The symbol in this situation is an element of a noncommutative algebra (crossed product by G) and to obtain an index formula, we define the Chern character for this algebra in the framework of noncommutative geometry.
LA - eng
KW - Nonlocal operator; Basic cohomology; Crossed product; Transverse ellipticity; Chern character; Index formula; nonlocal operator; basic cohomology; crossed product; transverse ellipticity; index formula; Fredholm index
UR - http://eudml.org/doc/269233
ER -

References

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