Jump to ContentJump to Main Navigation
Show Summary Details
More options …

Journal für die reine und angewandte Mathematik

Managing Editor: Weissauer, Rainer

Ed. by Colding, Tobias / Huybrechts, Daniel / Hwang, Jun-Muk / Williamson, Geordie


IMPACT FACTOR 2017: 1.686

CiteScore 2018: 1.14

SCImago Journal Rank (SJR) 2018: 2.554
Source Normalized Impact per Paper (SNIP) 2018: 1.411

Mathematical Citation Quotient (MCQ) 2017: 1.49

Online
ISSN
1435-5345
See all formats and pricing
More options …
Volume 2008, Issue 614

Issues

Invariant subspaces of nilpotent linear operators, I

Claus Michael Ringel / Markus Schmidmeier
Published Online: 2008-02-05 | DOI: https://doi.org/10.1515/CRELLE.2008.001

Abstract

Let k be a field. We consider triples (V, U, T), where V is a finite dimensional k-space, U a subspace of V and T : VV a linear operator with Tn = 0 for some n, and such that T(U) U. Thus, T is a nilpotent operator on V, and U is an invariant subspace with respect to T. We will discuss the question whether it is possible to classify these triples. These triples (V, U, T) are the objects of a category with the Krull-Remak-Schmidt property, thus it will be suffcient to deal with indecomposable triples. Obviously, the classification problem depends on n, and it will turn out that the decisive case is n = 6. For n < 6, there are only finitely many isomorphism classes of indecomposable triples, whereas for n > 6 we deal with what is called “wild” representation type, so no complete classification can be expected. For n = 6, we will exhibit a complete description of all the indecomposable triples.

About the article

Received: 2006-08-28

Published Online: 2008-02-05

Published in Print: 2008-01-01


Citation Information: Journal für die reine und angewandte Mathematik (Crelles Journal), Volume 2008, Issue 614, Pages 1–52, ISSN (Online) 1435-5345, ISSN (Print) 0075-4102, DOI: https://doi.org/10.1515/CRELLE.2008.001.

Export Citation

Citing Articles

Here you can find all Crossref-listed publications in which this article is cited. If you would like to receive automatic email messages as soon as this article is cited in other publications, simply activate the “Citation Alert” on the top of this page.

[1]
Grzegorz Bobiński and Jan Schröer
Journal of Algebra, 2018
[2]
Piotr Dowbor, Hagen Meltzer, and Markus Schmidmeier
Journal of Pure and Applied Algebra, 2018
[3]
Albert Compta, Josep Ferrer, and Marta Peña
Linear Algebra and its Applications, 2018
[4]
Miantao Liu, Ruixin Li, and Nan Gao
Algebra Colloquium, 2018, Volume 25, Number 03, Page 377
[5]
Wei Hu, Xiu-Hua Luo, Bao-Lin Xiong, and Guodong Zhou
Journal of Pure and Applied Algebra, 2018
[6]
Justyna Kosakowska and Markus Schmidmeier
Mathematische Zeitschrift, 2018
[7]
Bao-Lin Xiong, Pu Zhang, and Yue-Hui Zhang
Journal of Algebra, 2018
[8]
Keyan Song, Liusan Wu, and Yuehui Zhang
Communications in Algebra, 2017, Page 1
[10]
Justyna Kosakowska and Markus Schmidmeier
Journal of Algebra, 2017, Volume 491, Page 241
[11]
Xiu-Hua Luo and Pu Zhang
Journal of Algebra, 2017, Volume 479, Page 1
[12]
Christof Geiss, Bernard Leclerc, and Jan Schröer
Inventiones mathematicae, 2017, Volume 209, Number 1, Page 61
[13]
Tobias Rossmann
Mathematische Annalen, 2017, Volume 368, Number 1-2, Page 391
[14]
Nan Gao and Chrysostomos Psaroudakis
Algebras and Representation Theory, 2017, Volume 20, Number 2, Page 487
[15]
Keyan Song and Yuehui Zhang
Frontiers of Mathematics in China, 2016, Volume 11, Number 2, Page 401
[16]
[17]
Pin Liu and Ming Lu
Communications in Algebra, 2015, Volume 43, Number 6, Page 2443
[19]
A. Compta and J. Ferrer
Linear and Multilinear Algebra, 2015, Volume 63, Number 9, Page 1768
[20]
Claus Michael Ringel and Pu Zhang
Mathematische Zeitschrift, 2014, Volume 278, Number 1-2, Page 55
[21]
Keyan Song, Fan Kong, and Pu Zhang
Communications in Algebra, 2014, Volume 42, Number 9, Page 3708
[22]
KeYan Song and YueHui Zhang
Science China Mathematics, 2014, Volume 57, Number 3, Page 477
[23]
Xiu-Hua Luo and Pu Zhang
Pacific Journal of Mathematics, 2013, Volume 264, Number 1, Page 163
[24]
Dirk Kussin, Helmut Lenzing, and Hagen Meltzer
Advances in Mathematics, 2013, Volume 237, Page 194
[25]
YueHui Zhang
Science China Mathematics, 2013, Volume 56, Number 3, Page 525
[26]
Markus Schmidmeier
Algebras and Representation Theory, 2012, Volume 15, Number 3, Page 449
[27]
Apostolos Beligiannis
Advances in Mathematics, 2011, Volume 226, Number 2, Page 1973
[28]
Xiao-Wu Chen
Mathematische Zeitschrift, 2012, Volume 270, Number 1-2, Page 43
[29]
[30]
Markus Schmidmeier
Mathematische Zeitschrift, 2011, Volume 268, Number 1-2, Page 211

Comments (0)

Please log in or register to comment.
Log in