23 citations · 112 across the 27 of their papers we have counts for
23 papers · 1 filter
From Quaternions to Pentarnions I: Algebra, geometry, and a spin model
Alireza Poshtkohi, Susanne Pumpluen
We introduce a family of five-dimensional non-flexible quadratic real algebras with canonical basis , in which changes the multip…
A parametrization of nonassociative Petit algebras up to equivalence
Monica Nevins, Susanne Pumpluen
Let be a cyclic Galois field extension of degree with . The nonassociative Petit algebras have recently emerged…
A parametrization of nonassociative cyclic algebras of prime degree
Monica Nevins, Susanne Pumpluen
We determine and explicitly parametrize the isomorphism classes of nonassociative quaternion algebras over a field of characteristic different from two, as well as the isomorphism…
A generalization of the first Tits construction
Thomas Moran, Susanne Pumpluen
Let be a field of characteristic not 2 or 3. The first Tits construction is a well-known tripling process to construct separable cubic Jordan algebras, especially Albert algebr…
The automorphisms of differential extensions of characteristic
Susanne Pumpluen
Nonassociative differential extensions are generalizations of associative differential extensions, either of a purely inseparable field extension of exponent one of a field …
Nonassociative cyclic algebras and the semiassociative Brauer monoid
S Pumpluen
We look at classes of semiassociative algebras, with an emphasis on those that canonically generalize associative (generalized) cyclic algebras, and at their behaviour in the semia…
Division algebras and MRD codes from skew polynomials
Daniel Thompson, Susanne Pumpluen
Let be a division algebra, finite-dimensional over its center, and a skew polynomial ring. Using skew polynomials , we construct division algebras and a ge…
The norm of a skew polynomial
Susanne Pumpluen, Daniel Thompson
Let be a finite-dimensional division algebra over its center and a skew polynomial ring. Under certain assumptions on and , the ring of central quotients $D…
The eigenspaces of twisted polynomials over cyclic field extensions
Adam Owen, Susanne Pumpluen
Let be a field and an automorphism of of order .Employing a nonassociative algebra, we study the eigenspace of a bounded skew polynomial . We mainly tre…
Irreducible skew polynomials over domains
Christian Brown, Susanne Pumpluen
Let be a domain and a skew polynomial ring, where is an injective endomorphism of and a left -derivation. We give criteria for skew polynomials $f\…
The automorphisms of Petit's algebras
Christian Brown, Susanne Pumpluen
Let be an automorphism of a field with fixed field . We study the automorphisms of nonassociative unital algebras which are canonical generalizations of the associative…
Automorphisms and isomorphisms of Jha-Johnson semifields obtained from skew polynomial rings
Christian Brown, Susanne Pumpluen, Andrew Steele
We study the automorphisms of Jha-Johnson semifields obtained from an invariant irreducible twisted polynomial , where is a finite field and a…
Solvable crossed product algebras revisited
Christian Brown, Susanne Pumpluen
For any central simple algebra over a field F which contains a maximal subfield M with non-trivial F-automorphism group G, G is solvable if and only if the algebra contains a finit…
Quotients of orders in algebras obtained from skew polynomials with applications to coding theory
Susanne Pumpluen
We describe families of nonassociative finite unital rings that occur as quotients of natural nonassociative orders in generalized nonassociative cyclic division algebras over numb…
Nonassociative differential extensions of characteristic p
Susanne Pumpluen
Let F be a field of characteristic p. We define and investigate nonassociative differential extensions of F and of a central simple division algebra over F and give a criterium for…
Algebras whose right nucleus is a central simple algebra
Susanne Pumpluen
We generalize Amitsur's construction of central simple algebras over a field which are split by field extensions possessing a derivation with field of constants to nonassoc…
Tensor products of nonassociative cyclic algebras
Susanne Pumpluen
We study the tensor product of an associative and a nonassociative cyclic algebra. The condition for the tensor product to be a division algebra equals the classical one for the te…
How to obtain division algebras from a generalized Cayley-Dickson doubling process
Susanne Pumpluen
New families of eight-dimensional real division algebras with large derivation algebra are presented: We generalize the classical Cayley-Dickson doubling process starting with a un…
Albert algebras over curves of genus zero and one
Susanne Pumpluen
Albert algebras and other Jordan algebras are constructed over curves of genus zero and one, using a generalization of the Tits process and the first Tits construction due to Achha…
Jordan algebras over algebraic varieties
Susanne Pumpluen
We construct Jordan algebras over a locally ringed space using generalizations of the Tits process and the first Tits construction by Achhammer. Some general results on the structu…
Some classes of multiplicative forms of higher degree
S. Pumpluen
Several notions of multiplicativity are introduced for forms of degree over a field of characteristic 0 or greater than d. Examples of multiplicative and strongly multipl…
Forms of higher degree permitting composition
S. Pumpluen
Nondegenerate forms N of degree d on a unital nonassociative algebra A over a ring R which permit composition, i.e., satisfy N(1)=1 and N(xy)=N(x)N(y) for all x,y in A, are studied…
On flexible quadratic algebras
S. Pumpluen
Let R be a ring. A construction method for flexible quadratic algebras with scalar involution over R is presented which unifies various classical constructions in the literature, i…