Abstract
Abstract
We prove analogues of Schur’s lemma for endomorphisms of extensions in Tannakian categories. More precisely, let
$\mathbf {T}$
be a neutral Tannakian category over a field of characteristic zero. Let E be an extension of A by B in
$\mathbf {T}$
. We consider conditions under which every endomorphism of E that stabilises B induces a scalar map on
$A\oplus B$
. We give a result in this direction in the general setting of arbitrary
$\mathbf {T}$
and E, and then a stronger result when
$\mathbf {T}$
is filtered and the associated graded objects to A and B satisfy some conditions. We also discuss the sharpness of the results.
Publisher
Cambridge University Press (CUP)
Reference10 articles.
1. [5] Eskandari, P. and Kumar Murty, V. , ‘The fundamental group of an extension in a Tannakian category and the unipotent radical of the Mumford–Tate group of an open curve’, Pacific J. Math., to appear.
2. [8] Hardouin, C. , ‘Hypertranscendance et groupes de Galois aux différences’, Preprint, 2006, arXiv:0609646v2.
3. Unipotent radicals of differential Galois group and integrals of solutions of inhomogeneous equations;Bertrand;Math. Ann.,2001
4. Tannakian Categories
5. [4] Eskandari, P. , ‘On blended extensions in filtered Tannakian categories and mixed motives with maximal unipotent radicals’, Preprint, 2023, arXiv:2307.15487.
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1. ON ENDOMORPHISMS OF EXTENSIONS IN TANNAKIAN CATEGORIES;Bulletin of the Australian Mathematical Society;2023-11-07