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Lie Groups and Representation Theory
Seminar information archive ～04/25｜Next seminar｜Future seminars 04/26～
| Date, time & place | Tuesday 16:30 - 18:00 126Room #126 (Graduate School of Math. Sci. Bldg.) |
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2022/02/22
17:00-18:00 Room #online (Graduate School of Math. Sci. Bldg.)
Hiroyoshi Tamori (Hokkaido University)
On a long exact sequence of the Schwartz homology (Japanese)
Hiroyoshi Tamori (Hokkaido University)
On a long exact sequence of the Schwartz homology (Japanese)
[ Abstract ]
For a smooth Fr\’{e}chet representation of moderate growth of an almost linear Nash group, Chen-Sun introduced a homology (called Schwartz homology) equipped with certain topology. Given a short exact sequence of such representations, we can construct a long exact sequence of Schwartz homology groups via the natural isomorphism with relative Lie algebra homology. We give an example of a long exact sequence where the connecting homomorphism is not continuous.
For a smooth Fr\’{e}chet representation of moderate growth of an almost linear Nash group, Chen-Sun introduced a homology (called Schwartz homology) equipped with certain topology. Given a short exact sequence of such representations, we can construct a long exact sequence of Schwartz homology groups via the natural isomorphism with relative Lie algebra homology. We give an example of a long exact sequence where the connecting homomorphism is not continuous.
