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pro vyhledávání: '"Repka, Joe"'
Autor:
Douglas, Andrew, Repka, Joe
Let $\mathfrak{s}$ $\ltimes$ $\mathfrak{r}$ be a Levi decomposable Lie algebra, with Levi factor $\mathfrak{s}$, and radical $\mathfrak{r}$. A module $V$ of $\mathfrak{s}$ $\ltimes$ $\mathfrak{r}$ is cyclic indecomposable if it is indecomposable and
Externí odkaz:
http://arxiv.org/abs/2404.07372
Autor:
Douglas, Andrew, Repka, Joe
A subalgebra of a semisimple Lie algebra is wide if every simple module of the semisimple Lie algebra remains indecomposable when restricted to the subalgebra. A subalgebra is narrow if the restrictions of all non-trivial simple modules to the subalg
Externí odkaz:
http://arxiv.org/abs/2403.17951
Autor:
Douglas, Andrew, Repka, Joe
A subalgebra of a semisimple Lie algebra is wide if every simple module of the semisimple Lie algebra remains indecomposable when restricted to the subalgebra. From a finer viewpoint, a subalgebra is $\lambda$-wide if the simple module of a semisimpl
Externí odkaz:
http://arxiv.org/abs/2403.18847
Autor:
Douglas, Andrew, Repka, Joe
Publikováno v:
In Journal of Algebra 15 February 2025 664 Part A:348-361
Autor:
Douglas, Andrew, Repka, Joe
In this expository article, we describe the classification of the subalgebras of the rank 2 semisimple Lie algebras. Their semisimple subalgebras are well-known, and in a recent series of papers, we completed the classification of the subalgebras of
Externí odkaz:
http://arxiv.org/abs/1705.03600
Autor:
Douglas, Andrew, Repka, Joe
The semisimple subalgebras of the rank $2$ symplectic Lie algebra $\mathfrak{sp}(4,\mathbb{C})$ are well-known, and we recently classified its Levi decomposable subalgebras. In this article, we classify the solvable subalgebras of $\mathfrak{sp}(4,\m
Externí odkaz:
http://arxiv.org/abs/1704.00241
Autor:
Douglas, Andrew, Repka, Joe
A classification of the semisimple subalgebras of the Lie algebra of traceless $3\times 3$ matrices with complex entries, denoted $A_2$, is well-known. We classify its nonsemisimple subalgebras, thus completing the classification of the subalgebras o
Externí odkaz:
http://arxiv.org/abs/1509.00932
Let $\A$ be an algebra and $\sigma$ an automorphism of $\A$. A linear map $d$ of $\A$ is called a $\sigma$-derivation of $\A$ if $d(xy) = d(x)y + \sigma(x)d(y)$, for all $x, y \in \A$. A bilinear map $D: \A \times \A \to \A$ is said to be a $\sigma$-
Externí odkaz:
http://arxiv.org/abs/1312.3980
An abelian extension of the special orthogonal Lie algebra $D_n$ is a nonsemisimple Lie algebra $D_n \inplus V$, where $V$ is a finite-dimensional representation of $D_n$, with the understanding that $[V,V]=0$. We determine all abelian extensions of
Externí odkaz:
http://arxiv.org/abs/1305.6996
Autor:
Douglas, Andrew, Repka, Joe
Publikováno v:
SIGMA 10 (2014), 072, 10 pages
The (real) GraviGUT algebra is an extension of the $\mathfrak{spin}(11,3)$ algebra by a $64$-dimensional Lie algebra, but there is some ambiguity in the literature about its definition. Recently, Lisi constructed an embedding of the GraviGUT algebra
Externí odkaz:
http://arxiv.org/abs/1305.6946