### Abstract

There is a well-known interpretation of group cohomology in terms of (generalized) group extensions. For a connected semisimple compact Lie group K, we prove that the extensions corresponding to classes in H ^{4}(BK,ℤ) can be interpreted in terms of automorphisms of a pair consisting of a type II_{1} von Neumann algebra and a Cartan subalgebra.

Original language | English (US) |
---|---|

Pages (from-to) | 199-213 |

Number of pages | 15 |

Journal | Journal of Lie Theory |

Volume | 14 |

Issue number | 1 |

State | Published - 2004 |

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### ASJC Scopus subject areas

- Algebra and Number Theory

### Cite this

**H ^{4}(BK,Z) and Operator Algebras.** / Pickrell, Douglas M.

Research output: Contribution to journal › Article

^{4}(BK,Z) and Operator Algebras',

*Journal of Lie Theory*, vol. 14, no. 1, pp. 199-213.

}

TY - JOUR

T1 - H4(BK,Z) and Operator Algebras

AU - Pickrell, Douglas M

PY - 2004

Y1 - 2004

N2 - There is a well-known interpretation of group cohomology in terms of (generalized) group extensions. For a connected semisimple compact Lie group K, we prove that the extensions corresponding to classes in H 4(BK,ℤ) can be interpreted in terms of automorphisms of a pair consisting of a type II1 von Neumann algebra and a Cartan subalgebra.

AB - There is a well-known interpretation of group cohomology in terms of (generalized) group extensions. For a connected semisimple compact Lie group K, we prove that the extensions corresponding to classes in H 4(BK,ℤ) can be interpreted in terms of automorphisms of a pair consisting of a type II1 von Neumann algebra and a Cartan subalgebra.

UR - http://www.scopus.com/inward/record.url?scp=1542290878&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=1542290878&partnerID=8YFLogxK

M3 - Article

VL - 14

SP - 199

EP - 213

JO - Journal of Lie Theory

JF - Journal of Lie Theory

SN - 0949-5932

IS - 1

ER -