Zobrazeno 1 - 10
of 105
pro vyhledávání: '"Dietrich Burde"'
Publikováno v:
International Journal of Algebra and Computation. 32:1495-1511
We study rigidity questions for pairs of Lie algebras $(\mathfrak{g},\mathfrak{n})$ admitting a post-Lie algebra structure. We show that if $\mathfrak{g}$ is semisimple and $\mathfrak{n}$ is arbitrary, then we have rigidity in the sense that $\mathfr
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::0f6fba662d597a18c60f00bf749db1c6
https://doi.org/10.1142/s0218196722500679
https://doi.org/10.1142/s0218196722500679
Publikováno v:
Linear Algebra and its Applications. 608:185-202
We study almost inner derivations of 2-step nilpotent Lie algebras of genus 2, i.e., having a 2-dimensional commutator ideal, using matrix pencils. In particular we determine all almost inner derivations of such algebras in terms of minimal indices a
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::ece09755f5d130e4299e34d6f5f19fb3
https://doi.org/10.1016/j.laa.2020.08.023
https://doi.org/10.1016/j.laa.2020.08.023
Autor:
Christof Ender, Dietrich Burde
Publikováno v:
Linear Algebra and its Applications. 584:107-126
We give an explicit description of commutative post-Lie algebra structures on some classes of nilpotent Lie algebras. For non-metabelian filiform nilpotent Lie algebras and Lie algebras of strictly upper-triangular matrices we show that all CPA-struc
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::bd52b837929f661551b76b7de4a1fdc6
https://doi.org/10.1016/j.laa.2019.09.010
https://doi.org/10.1016/j.laa.2019.09.010
The abstract is available here: https://uscholar.univie.ac.at/o:1632683
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::f7df2949c0fae455a6ba56143e555314
https://hdl.handle.net/11353/10.1632683
https://hdl.handle.net/11353/10.1632683
Autor:
Vsevolod Gubarev, Dietrich Burde
Publikováno v:
International Journal of Algebra and Computation. 30:451-466
We introduce post-associative algebra structures and study their relationship to post-Lie algebra structures, Rota–Baxter operators and decompositions of associative algebras and Lie algebras. We show several results on the existence of such struct
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::64065cd6acd956c87781419a7b4269ce
https://doi.org/10.1142/s0218196720500071
https://doi.org/10.1142/s0218196720500071
Autor:
Dietrich Burde
Publikováno v:
Communications in Mathematics, Vol 29, Iss 1, Pp 67-89 (2021)
This survey on crystallographic groups, geometric structures on Lie groups and associated algebraic structures is based on a lecture given in the Ostrava research seminar in 2017.
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::5cb3611a501395a9b6318f6a8951ae72
https://phaidra.univie.ac.at/o:1417311
https://phaidra.univie.ac.at/o:1417311
Commutative post-Lie algebra structures on Lie algebras, in short CPA structures, have been studied over fields of characteristic zero, in particular for real and complex numbers motivated by geometry. A perfect Lie algebra in characteristic zero onl
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::44ea767ca8f1dbb994259a79c4f695a9
http://arxiv.org/abs/2001.04822
http://arxiv.org/abs/2001.04822
Publikováno v:
International Journal of Algebra and Computation. 28:915-933
We study post-Lie algebra structures on $(\mathfrak{g},\mathfrak{n})$ for nilpotent Lie algebras. First we show that if $\mathfrak{g}$ is nilpotent such that $H^0(\mathfrak{g},\mathfrak{n})=0$, then also $\mathfrak{n}$ must be nilpotent, of bounded c
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::59d54e890d1304801e928445b2daa512
https://doi.org/10.1142/s0218196718500406
https://doi.org/10.1142/s0218196718500406
Autor:
Dietrich Burde, Friedrich Wagemann
We study sympathetic Lie algebras, namely perfect and complete Lie algebras. They arise among other things in the study of adjoint Lie algebra cohomology. This is motivated by a conjecture of Pirashvili, which says that a non-trivial finite-dimension
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::e77cdc746cfc3ccec24fe1614cbdc0cf
http://arxiv.org/abs/1908.05963
http://arxiv.org/abs/1908.05963
We show that for a given nilpotent Lie algebra g with Z ( g ) ⊆ [ g , g ] all commutative post-Lie algebra structures, or CPA-structures, on g are complete. This means that all left and all right multiplication operators in the algebra are nilpoten
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::08af4d681e80f1c654f8ead1002b9b96
https://lirias.kuleuven.be/handle/123456789/654107
https://lirias.kuleuven.be/handle/123456789/654107