scholarly journals Journal of Combinatorial Algebra

10.4171/jca ◽  
2020 ◽  
Keyword(s):  
Combinatorial Algebra

Special arrangements of lines: Codimension 2 ACM varieties in ℙ1 × ℙ1 × ℙ1

2019 ◽  
Vol 18 (04) ◽  
pp. 1950073 ◽  
Author(s):  
Giuseppe Favacchio ◽  
Elena Guardo ◽  
Beatrice Picone
Keyword(s):  
Point Of View ◽  
Arrangements Of Lines ◽  
Multiprojective Spaces ◽  
Combinatorial Algebra

In this paper, we investigate special arrangements of lines in multiprojective spaces. In particular, we characterize codimension 2 arithmetically Cohen–Macaulay (ACM) varieties in [Formula: see text], called varieties of lines. We also describe their ACM property from a combinatorial algebra point of view.

scholarly journals Combinatorial Algebra for second-quantized Quantum Theory

2010 ◽  
Vol 14 (4) ◽  
pp. 1209-1243 ◽  
Author(s):  
Pawel Blasiak ◽  
Gerard H.E. Duchamp ◽  
Andrzej Horzela ◽  
Karol A. Penson ◽  
Allan I. Solomon
Keyword(s):  
Quantum Theory ◽  
Combinatorial Algebra

scholarly journals Structure Coefficients of the Hecke Algebra of $(\mathcal{S}_{2n},\mathcal{B}_n)$

10.37236/3592 ◽  
2014 ◽  
Vol 21 (4) ◽  
Author(s):  
Omar Tout
Keyword(s):  
Symmetric Group ◽  
Group Algebra ◽  
Main Tool ◽  
Hecke Algebra ◽  
Natural Analogue ◽  
New Class ◽  
Finite Dimensional ◽  
Finite Dimensional Algebras ◽  
Combinatorial Algebra

The Hecke algebra of the pair $(\mathcal{S}_{2n},\mathcal{B}_n)$, where $\mathcal{B}_n$ is the hyperoctahedral subgroup of $\mathcal{S}_{2n}$, was introduced by James in 1961. It is a natural analogue of the center of the symmetric group algebra. In this paper, we give a polynomiality property of its structure coefficients. Our main tool is a combinatorial algebra which projects onto the Hecke algebra of $(\mathcal{S}_{2n},\mathcal{B}_n)$ for every $n$. To build it, by using partial bijections we introduce and study a new class of finite dimensional algebras.

Use of combinatorial algebra for diffusion on fractals

1986 ◽  
Vol 34 (3) ◽  
pp. 2501-2504 ◽  
Author(s):  
Akhlesh Lakhtakia ◽  
Russell Messier ◽  
Vijay K. Varadan ◽  
Vasundara V. Varadan
Keyword(s):  
Combinatorial Algebra

Combinatorial Algebra and Its Antisymmetrized Algebra I

2015 ◽  
Vol 22 (spec01) ◽  
pp. 823-834
Author(s):  
Seul Hee Choi ◽  
Hong Goo Park ◽  
Moon-Ok Wang ◽  
Ki-Bong Nam
Keyword(s):  
Lie Algebra ◽  
Associative Algebra ◽  
Algebra I ◽  
Combinatorial Algebra

The simple non-associative algebra N(eAS, q, n, t)k and its simple subalgebras are defined in [1, 3, 5–7, 13]. In this work, we define the combinatorial algebra N(e𝔄p, n, t)k and its antisymmetrized algebra [Formula: see text] and their subalgebras. We prove that these algebras are simple. Some authors [2, 5–7, 10, 13, 14, 16, 17] found all the derivations of an associative algebra, a Lie algebra, and a non-associative algebra. We find all the derivations of the subalgebra N(e±x1x2 ⋯xn, 0, n)[1] of N(e𝔄p, n, t)k and the Lie subalgebra [Formula: see text] of [Formula: see text].

scholarly journals The word problem for one-relation monoids: a survey

2021 ◽  
Author(s):  
Carl-Fredrik Nyberg-Brodda
Keyword(s):  
Word Problem ◽  
Open Problems ◽  
Inverse Monoids ◽  
Collatz Conjecture ◽  
History Of ◽  
The Way ◽  
Combinatorial Algebra

AbstractThis survey is intended to provide an overview of one of the oldest and most celebrated open problems in combinatorial algebra: the word problem for one-relation monoids. We provide a history of the problem starting in 1914, and give a detailed overview of the proofs of central results, especially those due to Adian and his student Oganesian. After showing how to reduce the problem to the left cancellative case, the second half of the survey focuses on various methods for solving partial cases in this family. We finish with some modern and very recent results pertaining to this problem, including a link to the Collatz conjecture. Along the way, we emphasise and address a number of incorrect and inaccurate statements that have appeared in the literature over the years. We also fill a gap in the proof of a theorem linking special inverse monoids to one-relation monoids, and slightly strengthen the statement of this theorem.

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