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Orders in Quaternion Algebras [PDF]
, 2003 The basic algebraic theory of quaternion algebras was given in Chapter 2. That sufficed for the results obtained so far on deducing information on a Kleinian group Γ from its invariant trace field kΓ and invariant quaternion algebra AΓ. We have yet to expound on the arithmetic theory of quaternion algebras over number fields.
C. Maclachlan, Alan W. Reid
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Quaternion algebras with derivations
Journal of Pure and Applied Algebra, 2022Abstract We study derivations on quaternion algebras that stabilise quadratic subfields. Following the work of L. Juan and A. Magid [10] , we provide an explicit construction of a differential splitting field for a given differential quaternion algebra.
Varadharaj R. Srinivasan +1 more
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2003
One of the main aims of this chapter is to complete the classification theorem for quaternion algebras over a number field by establishing the existence part of that theorem. This theorem, together with other results in this chapter, make use of the rings of adeles and groups of ideles associated to number fields and quaternion algebras.
C. Maclachlan, Alan W. Reid
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One of the main aims of this chapter is to complete the classification theorem for quaternion algebras over a number field by establishing the existence part of that theorem. This theorem, together with other results in this chapter, make use of the rings of adeles and groups of ideles associated to number fields and quaternion algebras.
C. Maclachlan, Alan W. Reid
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Levels of quaternion algebras [PDF]
Archiv der Mathematik, 2008 The level of a ring R with 1 ≠ 0 is the smallest positive integer s such that −1 can be written as a sum of s squares in R, provided −1 is a sum of squares at all. D. W. Lewis showed that any value of type 2n or 2n + 1 can be realized as level of a quaternion algebra, and he asked whether there exist quaternion algebras whose levels are not of that ...
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On orders in quaternion algebras
Communications in Algebra, 1983(1983). On orders in quaternion algebras. Communications in Algebra: Vol. 11, No. 5, pp. 501-522.
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ON THE LEVEL OF A QUATERNION ALGEBRA
Communications in Algebra, 2001In [6] D. W. Lewis proved the existence of a quaternion division algebra of level 2 n or 2 n + 1 for any integer n ≥ 1. In this note, we present news examples of quaternion division algebras of such levels. We also recover a result of P. Koprowski [4]. Our method is different and based on function field of projective quadrics.
Pasquale Mammone, Ahmed Laghribi
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Division Algebras—Beyond the Quaternions
The American Mathematical Monthly, 1998(1998). Division Algebras—Beyond the Quaternions. The American Mathematical Monthly: Vol. 105, No. 2, pp. 154-162.
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Algebras, Quaternions and Quaternionic Symplectic Groups
2002In this chapter we begin by studying algebras over a field, with their groups of units providing many interesting groups. In particular, we study division algebras and their linear algebra. Then we introduce the quaternions which form the only non-commutative example of a real division algebra.
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Submodules of Quaternion Algebras [PDF]
Proceedings of the London Mathematical Society, 1969 openaire +1 more source