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Divsion Algorithm and Construction of Curves with Many Points
(Universidad Nacional de Colombia, 2013-12)
We give a simple and effective method for the construction of
algebraic curves over finite fields with many rational points. The curves are
given as Kummer covers of the projective line.
Computing ideal classes representatives in quaternion algebras
(American Mathematical Society, 2014-06)
Let K be a totally real number field and let B be a totally definite quaternion algebra over K. Given a set of representatives for ideal classes for a maximal order in B, we show how to construct in an efficient way a set ...
Nilpotency degree of the nilradical of a solvable Lie algebra on two generators and uniserial modules associated to free nilpotent Lie algebras
(Academic Press Inc Elsevier Science, 2021-11-20)
Given a sequence d~ = (d1, . . . , dk) of natural numbers, we consider
the Lie subalgebra h of gl(d, F), where d = d1 + · · · + dk and F is a field of
characteristic 0, generated by two block upper triangular matrices D ...
Nonsemisimple Hopf algebras of dimension 8p with the Chevalley property
(American Mathematical Society, 2019-04)
Let p be an odd prime and k an algebraically closed field of characteristiczero. We classify nonsemisimple Hopf algebras over k of dimension8p with the Chevalley property, and give partial results on nonsemisimple Hopfalgebras ...
Jacobi-Zariski long nearly exact sequences for associative algebras
(Wiley, 2021-06)
For an extension of associative algebras (Formula presented.) over a field and an (Formula presented.) -bimodule (Formula presented.), we obtain a Jacobi–Zariski long nearly exact sequence relating the Hochschild homologies ...
Examples of finite-dimensional pointed Hopf algebras in characteristic 2
(Cambridge University Press, 2020-12-01)
We present new examples of finite-dimensional Nichols algebras over fields of characteristic 2 from braided vector spaces that are not of diagonal type, admit realizations as Yetter-Drinfeld modules over finite abelian ...
Hochschild cohomology of triangular matrix algebras
(Academic Press Inc Elsevier Science, 2000-11)
We study the Hochschild cohomology of triangular matrix rings B=R0AMRA , where A and R are finite dimensional algebras over an algebraically closed field K and M is an A-R-bimodule. We prove the existence of two long exact ...
L ∞ algebras and tensor hierarchies in Exceptional Field Theory and Gauged Supergravity
(Springer, 2019-01)
We show how the gauge and field structure of the tensor hierarchies in Double and E7(7) Exceptional Field Theory fits into L∞ algebras. Special attention is paid to redefinitions, the role of covariantly constrained fields ...
Covering functors without groups
(Academic Press Inc Elsevier Science, 2009-06)
Coverings in the representation theory of algebras were introduced for the Auslander-Reiten quiver of a representation-finite algebra in [Ch. Riedtmann, Algebren, Darstellungsköcher, Überlagerungen und zurüch, Comment. ...
On the Tits-Weiss conjecture and the Kneser-Tits conjecture for E_78^ 7,1 and E_78^8,2 (With an Appendix by R. M. Weiss)
(Cambridge University Press, 2021-11)
We prove that the structure group of any Albert algebra over an arbitrary field is R-trivial. This implies the Tits-Weiss conjecture for Albert algebras and the Kneser-Tits conjecture for isotropic groups of type E78 7,1 ...