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IP 1115-05-645-9
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IP 1115-05-420-9
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The varieties of dialgebras (also known as Loday-type algebras) over a given type of algebra have been the subject of multiple recent developments. We provide here a construction of such dialgebra varieties via bimodules over an algebra... more
The varieties of dialgebras (also known as Loday-type algebras) over a given type of algebra have been the subject of multiple recent developments. We provide here a construction of such dialgebra varieties via bimodules over an algebra and a surjective equivariant map. Our construction is equivalent to the KP construction (Kolesnikov–Pozhidaev construction) when departing from the set of linearized identities of the algebra variety. The novel construction simplifies the obtention of the dialgebra equations without forcing a complete linearization of the algebra identities. We illustrate the use of the novel construction providing the dialgebras associated to several varieties of algebras, including those over diverse Lie admissible algebras. We provide some novel explorations on the structure of the dialgebras which are easily articulated through our construction.
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The concept of digroup has been proposed as a generalization of continuous groups whose tangent space is a Leibniz algebra. We study a further generalization of the digroup structure in which we do not demand that the inverses are... more
The concept of digroup has been proposed as a generalization of continuous groups whose tangent space is a Leibniz algebra. We study a further generalization of the digroup structure in which we do not demand that the inverses are necessarily bilateral. We characterize a generalized digroup as a set and as a product. We show an analogous to the first isomorphism theorem. Additionally, we explore the concept of dialgebra digroup.
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Abstract. We study graded algebras with no monomial in the generators having zero divisors and graded over a finite abelian group. As a vector space over the field, the algebra is generated by a set of algebra elements with as many... more
Abstract. We study graded algebras with no monomial in the generators having zero divisors and graded over a finite abelian group. As a vector space over the field, the algebra is generated by a set of algebra elements with as many elements as the grading group, and each generator is graded by a different element of the grading group. Their noncommutativity and nonassociativity turns out to be diagonal and governed by structure con-stants of any (pure grade) generating basis as a vector space over the field. There are functions q and r coding the noncommutativity and nonassocia-tivity of the algebra. We study the cohomology of such q- and r-functions. We discover that the r-function coding nonassociativity has always trivial cohomology. Quaternions and octonions are constructed in this manner and we study their noncommutativity and nonassociativity using cohomo-logical tools. 1.
We discuss the notion of normality of a sub-object in the category of digroups. This allows us to define quotient digroups, and then establish the corresponding analogues of the classical Isomorphism Theorems.
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We study graded algebras with no monomial in the generators having zero divisors and graded over a finite abelian group. As a vector space over the field, the algebra is generated by a set of algebra elements with as many elements as the... more
We study graded algebras with no monomial in the generators having zero divisors and graded over a finite abelian group. As a vector space over the field, the algebra is generated by a set of algebra elements with as many elements as the grading group, and each generator is graded by a different element of the grading group. Their noncommutativity and nonassociativity turns out to be diagonal and governed by structure constants of any (pure grade) generating basis as a vector space over the field. There are functions q and r coding the noncommutativity and nonassociativity of the algebra. We study the cohomology of such qand r-functions. We discover that the r-function coding nonassociativity has always trivial cohomology. Quaternions and octonions are constructed in this manner and we study their noncommutativity and nonassociativity using cohomological tools.
Consistent algebraic extensions of the Poincare´ algebra are obtained in which the novel generators can act with commutators or anticommutators on the Poincare´ generators.
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Mode of access: World Wide Web. Thesis (Ph. D.)--University of Hawaii at Manoa, 2004. Includes bibliographical references (leaves 159-164). Electronic reproduction. Also available by subscription via World Wide Web x, 164 leaves, bound... more
Mode of access: World Wide Web. Thesis (Ph. D.)--University of Hawaii at Manoa, 2004. Includes bibliographical references (leaves 159-164). Electronic reproduction. Also available by subscription via World Wide Web x, 164 leaves, bound ill. 29 cm
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We study graded algebras with no monomial in the generators having zero divisors and graded over a finite abelian group. As a vector space over the field, the algebra is generated by a set of algebra elements with as many elements as the... more
We study graded algebras with no monomial in the generators having zero divisors and graded over a finite abelian group. As a vector space over the field, the algebra is generated by a set of algebra elements with as many elements as the grading group, and each generator is graded by a different element of the grading group. Their noncommutativity and nonassociativity turns out to be diagonal and governed by structure con-stants of any (pure grade) generating basis as a vector space over the field. There are functions q and r coding the noncommutativity and nonassocia-tivity of the algebra. We study the cohomology of such q-and r-functions. We discover that the r-function coding nonassociativity has always trivial cohomology. Quaternions and octonions are constructed in this manner and we study their noncommutativity and nonassociativity using cohomo-logical tools.
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ABSTRACT We discuss the construction of parameter algebras compatible with the underlying graded structure of Special Relativity. The existence of associative and nonassociative Z2×(Z4Λ×Z4Λ)-graded parameter algebras is thoroughly... more
ABSTRACT We discuss the construction of parameter algebras compatible with the underlying graded structure of Special Relativity. The existence of associative and nonassociative Z2×(Z4Λ×Z4Λ)-graded parameter algebras is thoroughly analyzed. The corresponding enlarged Lie algebraic structures are presented.
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We construct a novel graded extension of the Poincare´ group with integer spin multiplets as novel generators. The extension involves Z4×Z4 graded parameters and produce space–time translations through the composition of novel symmetric... more
We construct a novel graded extension of the Poincare´ group with integer spin multiplets as novel generators. The extension involves Z4×Z4 graded parameters and produce space–time translations through the composition of novel symmetric vector and scalar multiplets.
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ABSTRACT A graded minimal Lie algebraic extension of the space-time symmetry is constructed involving only spin-1 multiplets as novel generators. The extension involves ℤ 4 ×ℤ 4 graded parameters and generators. It provides a bosonic... more
ABSTRACT A graded minimal Lie algebraic extension of the space-time symmetry is constructed involving only spin-1 multiplets as novel generators. The extension involves ℤ 4 ×ℤ 4 graded parameters and generators. It provides a bosonic analog to supersymmetry since the composition of three symmetric vector charges produces a space-time translation. There arise three noncommutative four-dimensional manifolds with pseudometric. Parts II and III, cf. ibid. 42, No. 8, 3935–3946, 3947–3964 (2001; Zbl 1063.81061 and Zbl 1064.81066).
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ABSTRACT The constraints on the index set I and on the function q of the (I,q)‐graded Lie algebras over K containing the Poincaré Lie algebra are studied. By using the single‐grading model, particular choices for I and q consistent with... more
ABSTRACT The constraints on the index set I and on the function q of the (I,q)‐graded Lie algebras over K containing the Poincaré Lie algebra are studied. By using the single‐grading model, particular choices for I and q consistent with the found constraints are determined for K=C. Gradings are then found for which I⊆I=Z2×(Z4N×Z4N)×Gre, with N∊N and Gre an Abelian group. These gradings provide a way for algebraic extensions of the Poincaré Lie algebra beyond the Z2‐gradings of supersymmetry and supergravity. In these algebraic extensions, each other commuting space–time parameter can either commute or anticommute with the further parameters of the (I,q)‐graded (super) manifold. Different field representations can have—with each other—generalized commutative behavior beyond commutativity and anticommutativity. © 1995 American Institute of Physics.