Results 41 to 50 of about 609,367 (341)

Chain equivalences for symplectic bases, quadratic forms and tensor products of quaternion algebras [PDF]

, 2013
We present a set of generators for the symplectic group which is different from the well-known set of transvections, from which the chain equivalence for quadratic forms in characteristic 2 is an immediate result.
Adam Chapman
semanticscholar   +1 more source

Definite orders with locally free cancellation

Transactions of the London Mathematical Society, 2019
We enumerate all orders in definite quaternion algebras over number fields with the Hermite property; this includes all orders with the cancellation property for locally free modules.
Daniel Smertnig, John Voight
doaj   +1 more source

Generalized Quaternions and Matrix Algebra

Afyon Kocatepe University Journal of Sciences and Engineering, 2023
In this paper, we established the connection between generalized quaternion algebra and real (complex) matrix algebras by using Hamilton operators. We obtained real and complex matrices corresponding to the real and complex basis of the generalized quaternions. Also, we investigated the basis features of real and complex matrices. We get Pauli matrices
Erhan ATA, Ümit Ziya SAVCI
openaire   +3 more sources

Linkage of sets of quaternion algebras in characteristic 2

, 2019
This note contains two new observations on the linkage properties of quaternion algebras over fields of characteristic 2: first, that a 3-linked field need not be 4-linked (a case which was left open in previous papers) and that three inseparably linked ...
Adam Chapman
semanticscholar   +1 more source

A Gross-Zagier formula for quaternion algebras over totally real fields [PDF]

IACR Cryptology ePrint Archive, 2011
We prove a higher dimensional generalization of Gross and Zagier's theorem on the factoriza- tion of differences of singular moduli. Their result is proved by giving a counting formula for the number of isomorphisms between elliptic curves with complex ...
E. Goren, K. Lauter
semanticscholar   +1 more source

Hyperkähler, bi-hypercomplex, generalized hyperkähler structures and T-duality

Nuclear Physics B, 2022
We exploit the doubled formalism to study comprehensive relations among T-duality, complex and bi-hermitian structures (J+,J−) in two-dimensional N=(2,2) sigma models with/without twisted chiral multiplets. The bi-hermitian structures (J+,J−) embedded in
Tetsuji Kimura, Shin Sasaki, Kenta Shiozawa   +2 more
doaj   +1 more source

Orthogonal symmetries and Clifford algebras [PDF]

, 2010
Involutions of the Clifford algebra of a quadratic space induced by orthogonal symmetries are investigated.Comment: 22 ...
Mahmoudi, M. G.
core   +2 more sources

Hopf algebra structures on generalized quaternion algebras

Electronic Research Archive
In this paper, we use elementary linear algebra methods to explore possible Hopf algebra structures within the generalized quaternion algebra. The sufficient and necessary conditions that make the generalized quaternion algebra a Hopf algebra are given ...
Quanguo Chen , Yong Deng
doaj   +1 more source

Jacobian algebras with periodic module category and exponential growth [PDF]

, 2015
The Jacobian algebra associated to a triangulation of a closed surface $S$ with a collection of marked points $M$ is (weakly) symmetric and tame. We show that for these algebras the Auslander-Reiten translate acts 2-periodical on objects.
Valdivieso-Díaz, Yadira
core   +2 more sources

Quaternionic lie algebras

Linear Algebra and its Applications, 1984
Let k be a field of characteristic not equal to 2, and let L be a finite field extension of k. Then a Lie algebra G is quaternionic if there is a quaternion division algebra Q over L such that G is isomorphic to the k- Lie-algebra \(Q^-/L1\). The main theorem of the paper gives equivalent conditions for a finite-dimensional Lie algebra over a perfect ...
openaire   +2 more sources