The functions studied in the paper are quaternion-valued of a quaternionic variable. It is shown that left slice regular and right related by particular involution, intrinsic play central role theory functions. relation between functions, revealed. As an application, classical Laplace transform generalized naturally to quaternions two different ways, which function real variable or function. us...

We study differential splitting fields of quaternion algebras with derivations. A algebra over a field k is always split by quadratic extension k. However, need not be any algebraic use solutions certain Riccati equations to provide bounds on the transcendence degree algebra.

در این مقاله فرم رد جیکوبسن را به فرم‌های هرمیتی پادمتقارن روی جبرهای تقسیم کواترنیون با برگردان متعامد در مشخصه‌ی دلخواه تعمیم می‌دهیم. با استفاده از این فرم تعمیم‌یافته، یک رده‌‌بندی از فرم‌های هرمیتی مذکور ارائه می‌نمائیم. همچنین نشان می‌دهیم یک فرم هرمیتی ایزوتروپ (متابولیک) است اگر و تنها اگر فرم رد جیکوبسن تعمیم‌یافته‌ی آن ایزوتروپ (متابولیک) باشد. .

For a family of local algebras of semidihedral type over an algebraically closed field of characteristic 2, the Hochschild cohomology algebra is described in terms of generators and relations. The calculations are based on the construction of a bimodule resolution for the algebras in question. As a consequence, the Hochschild cohomology algebra is described for the group algebras of semidihedra...

An important problem in analytic and geometric combinatorics is estimating the number of lattice points in a compact convex set in a Euclidean space. Such estimates have numerous applications throughout mathematics. In this note, we exhibit applications of a particular estimate of this sort to several counting problems in number theory: counting integral points and units of bounded height over ...

We extend the Siegel-Weil formula to all quaternion dual pairs. Applications include the classification problem of skew hermitian forms over a quaternion algebra over a number field and a product formula for the weighted average of the representation numbers of a skew hermitian form by another skew hermitian form.

We present in this paper some fundamental tools for developing matrix analysis over the complex quaternion algebra. As applications, we consider generalized inverses, eigenvalues and eigenvectors, similarity, determinants of complex quaternion matrices, and so on. AMS Mathematics Subject Classification: 15A06; 15A24; 15A33

Constructions of quaternion and octonion algebras, suggested to have new level and sublevel values, are proposed and justified. In particular, octonion algebras of level and sublevel 6 and 7 are constructed. In addition, Hoffmann’s proof of the existence of infinitely many new values for the level of a quaternion algebra is generalised and adapted.

We prove that the non-CM Q-abelian surfaces whose endomorphism algebra is a quaternion algebra are parametrized, up to isogeny, by the rational points of the quotient of certain Shimura curves by the group of their Atkin-Lehner involutions.