Finite-dimensional quasirepresentations of connected Lie groups and Mishchenko’s conjecture

Shtern, A. I.

doi:10.1007/s10958-009-9466-3

Cited by 31 publications

(2 citation statements)

References 155 publications

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“…The paper [18] is a very interesting survey of their contributions. The notion of quasirepresentation of a group is used in the literature in several non-equivalent contexts, to mean several different things, see [22].…”

Section: Introductionmentioning

confidence: 99%

Group quasi-representations and almost flat bundles

Dǎdǎrlat¹

2014

J. Noncommut. Geom.

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We study the existence of quasi-representations of discrete groups G into unitary groups U.n/ that induce prescribed partial maps K 0 .C .G// ! Z on the K-theory of the group C*-algebra of G. We give conditions for a discrete group G under which the K-theory group of the classifying space BG consists entirely of almost flat classes. (2010). 46L80, 46L65, 19K35, 19K56. Mathematics Subject Classification

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Section: Introductionmentioning

confidence: 99%

Group quasi-representations and almost flat bundles

Dǎdǎrlat¹

2014

J. Noncommut. Geom.

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“…Since the restriction of π to G * is continuous by Theorem IV and the identity on each irreducible subrepresentation of π by Lemma 7, it follows that the restriction of π to rad G * is continuous and is represented by upper triangular matrices with ones on the principal diagonal (see [9], [49]), and it follows from our condition of continuity that the restriction of π to O is also continuous and represented by upper triangular matrices with ones on the principal diagonal. Thus, the representation π is trivial on each compact subgroup of O, which proves that Proof.…”

Section: A Version Of Hochschild's Theoremmentioning

confidence: 99%

Connected locally compact groups: The Hochschild kernel and faithfulness of locally bounded finite-dimensional representations

Shtern

2011

Trans. Moscow Math. Soc.

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Abstract. We obtain a number of consequences of the theorem on the automatic continuity of locally bounded finite-dimensional representations of connected Lie groups on the derived subgroup of the group, as well as an analogue of Lie's theorem for (not necessarily continuous) finite-dimensional representations of connected soluble locally compact groups. In particular, we give a description of connected Lie groups admitting a (not necessarily continuous) faithful locally bounded finitedimensional representation; as it turns out, such groups are linear. Furthermore, we give a description of the intersection of the kernels of continuous finite-dimensional representations of a given connected locally compact group, obtain a generalization of Hochschild's theorem on the kernel of the universal representation in terms of locally bounded (not necessarily continuous) finite-dimensional linear representations, and find the intersection of the kernels of such representations for a connected reductive Lie group.

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Specific Properties of One-Dimensional Pseudorepresentations of Groups

Shtern

2018

J Math Sci

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Finite-dimensional quasirepresentations of connected Lie groups and Mishchenko’s conjecture

Cited by 31 publications

References 155 publications

Group quasi-representations and almost flat bundles

Group quasi-representations and almost flat bundles

Connected locally compact groups: The Hochschild kernel and faithfulness of locally bounded finite-dimensional representations

Specific Properties of One-Dimensional Pseudorepresentations of Groups

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