Results 41 to 50 of about 66,979 (212)
Cohomology of split algebras and of trivial extensions [PDF]
, 2001 We consider associative algebras L over a field provided with a direct sum decomposition of a two-sided ideal M and a sub-algebra A - examples are provided by trivial extensions or triangular type matrix algebras.
Cibils, Claude +3 more
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Waring problem for triangular matrix algebra
Linear Algebra and its ApplicationsThe Matrix Waring problem is if we can write every matrix as a sum of $k$-th powers. Here, we look at the same problem for triangular matrix algebra $T_n(\mathbb{F}_q)$ consisting of upper triangular matrices over a finite field. We prove that for all integers $k, n \geq 1$, there exists a constant $\mathcal C(k, n)$, such that for all $q> \mathcal ...
Kaushik, Rahul, Singh, Anupam
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Exceptional cycles in triangular matrix algebras
Journal of Algebra, 2023 An exceptional cycle in a triangulated category with Serre functor is a generalization of a spherical object. Suppose that $A$ and $B$ are Gorenstein algebras, given a perfect exceptional $n$-cycle $E_*$ in $K^b(A\mbox{-}{\rm proj})$ and a perfect exceptional $m$-cycle $F_*$ in $K^b(B\mbox{-}{\rm proj})$, we construct an $A$-$B$-bimodule $N$, and prove
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On kappa-deformation and triangular quasibialgebra structure [PDF]
, 2008 We show that, up to terms of order 1/kappa^5, the kappa-deformed Poincare algebra can be endowed with a triangular quasibialgebra structure. The universal R matrix and coassociator are given explicitly to the first few orders.
Agostini +58 more
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Tame triangular matrix algebras over self-injective algebras
Tsukuba Journal of Mathematics, 1987 Let A be a basic connected finite dimensional algebra over an algebraically closed field and \(T_ 2(A)\) be the algebra of \(2\times 2\) upper triangular matrices over A. It is known [the reviewer, Bull. Pol. Acad. Sci., Math. 34, 517-523 (1986; Zbl 0612.16016)] that, if \(T_ 2(A)\) is tame, then A is representation-finite. Here, one proves that, for A
Hoshino, Mitsuo, Miyachi, Jun-ichi
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Representations of Frobenius-type triangular matrix algebras [PDF]
Acta Mathematica Sinica, English Series, 2016 The aim of this paper is mainly to build a new representation-theoretic realization of finite root systems through the so-called Frobenius-type triangular matrix algebras by the method of reflection functors over any field. Finally, we give an analog of APR-tilting module for this class of algebras.
Li, Fang, Ye, Chang
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Quantum dynamical Yang-Baxter equation over a nonabelian base
, 2002 In this paper we consider dynamical r-matrices over a nonabelian base. There are two main results. First, corresponding to a fat reductive decomposition of a Lie algebra $\frakg =\frakh \oplus \frakm$, we construct geometrically a non-degenerate ...
Xu, Ping
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Minimal faithful upper-triangular matrix representations for solvable Lie algebras [PDF]
, 2017 A well-known result on Lie Theory states that every finite-dimensional complex solvable Lie algebra can be represented as a matrix Lie algebra, with upper-triangular square matrices as elements.
Ceballos González, Manuel +2 more
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Unitary Irreducible Representations of a Lie Algebra for Matrix Chain Models
, 2001 There is a decomposition of a Lie algebra for open matrix chains akin to the triangular decomposition. We use this decomposition to construct unitary irreducible representations. All multiple meson states can be retrieved this way. Moreover, they are the
Jakobsen, H. P., Lee, C. -W. H.
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Han's conjecture and Hochschild homology for null-square projective algebras [PDF]
, 2019 Let $\mathcal H$ be the class of algebras verifying Han's conjecture. In this paper we analyse two types of algebras with the aim of providing an inductive step towards the proof of this conjecture.
Cibils, Claude +2 more
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