Quaternion Algebras and Generalized Fibonacci–Lucas Quaternions
نویسندگان
چکیده
منابع مشابه
Arithmetics of Rational Generalized Quaternion Algebras
a0 is called the real part of Q. An arithmetic S of Q(a, ]8) is a set of numbers having the following properties : Ca : S is closed with respect to algebraic addition. Cm: S is closed with respect to multiplication. R: For every number of 5, (4) has integral coefficients. U: 5 contains I0 , Ii and I2 (and hence I i l 2 by Cm). M : 5 is maximal ; that is, S is contained in no larger set having P...
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The quaternion group Q8 is one of the two non-abelian groups of size 8 (up to isomorphism). The other one, D4, can be constructed as a semi-direct product: D4 ∼= Aff(Z/(4)) ∼= Z/(4) o (Z/(4))× ∼= Z/(4) o Z/(2), where the elements of Z/(2) act on Z/(4) as the identity and negation. While Q8 is not a semi-direct product, it can be constructed as the quotient group of a semi-direct product. We wil...
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The additive identity is (0, 0), the multiplicative identity is (1, 0), and from addition and scalar multiplication of real vectors we have (a, b) = (a, 0) + (0, b) = a(1, 0) + b(0, 1), which looks like a+ bi if we define i to be (0, 1). Real numbers occur as the pairs (a, 0). Hamilton asked himself if it was possible to multiply triples (a, b, c) in a nice way that extends multiplication of co...
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In terms of generators and defining relations, a description is given of the Hochschild cohomology algebra for one of the series of local algebras of quaternion type. As a corollary, the Hochschild cohomology algebra is described for the group algebras of generalized quaternion groups over algebraically closed fields of characteristic 2. Introduction Let R be a finite-dimensional algebra over a...
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ژورنال
عنوان ژورنال: Advances in Applied Clifford Algebras
سال: 2015
ISSN: 0188-7009,1661-4909
DOI: 10.1007/s00006-015-0542-0