Displaying similar documents to “From factorizations of noncommutative polynomials to combinatorial topology”

Hyperidentities in associative graph algebras

Tiang Poomsa-ard (2000)

Discussiones Mathematicae - General Algebra and Applications

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Graph algebras establish a connection between directed graphs without multiple edges and special universal algebras of type (2,0). We say that a graph G satisfies an identity s ≈ t if the correspondinggraph algebra A(G) satisfies s ≈ t. A graph G is called associative if the corresponding graph algebra A(G) satisfies the equation (xy)z ≈ x(yz). An identity s ≈ t of terms s and t of any type τ is called a hyperidentity of an algebra A̲ if whenever the operation symbols occurring in s...

On the classification of the real flexible division algebras

Erik Darpö (2006)

Colloquium Mathematicae

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We investigate the class of finite-dimensional real flexible division algebras. We classify the commutative division algebras, completing an approach by Althoen and Kugler. We solve the isomorphism problem for scalar isotopes of quadratic division algebras, and classify the generalised pseudo-octonion algebras. In view of earlier results by Benkart, Britten and Osborn and Cuenca Mira et al., this reduces the problem of classifying the real flexible division algebras...

Ringel-Hall algebras of hereditary pure semisimple coalgebras

Justyna Kosakowska (2009)

Colloquium Mathematicae

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We define and investigate Ringel-Hall algebras of coalgebras (usually infinite-dimensional). We extend Ringel's results [Banach Center Publ. 26 (1990) and Adv. Math. 84 (1990)] from finite-dimensional algebras to infinite-dimensional coalgebras.

On d -algebras

Joseph Neggers, Hee Sik Kim (1999)

Mathematica Slovaca

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On B-algebras

J. Neggers, Hee Sik Kim (2002)

Matematički Vesnik

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Directed pseudo-graphs and Lie algebras over finite fields

Luis B. Boza, Eugenio Manuel Fedriani, Juan Núñez, Ana María Pacheco, María Trinidad Villar (2014)

Czechoslovak Mathematical Journal

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The main goal of this paper is to show an application of Graph Theory to classifying Lie algebras over finite fields. It is rooted in the representation of each Lie algebra by a certain pseudo-graph. As partial results, it is deduced that there exist, up to isomorphism, four, six, fourteen and thirty-four 2 -, 3 -, 4 -, and 5 -dimensional algebras of the studied family, respectively, over the field ℤ / 2 ℤ . Over ℤ / 3 ℤ , eight and twenty-two 2 - and 3 -dimensional Lie algebras, respectively, are also...