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Books on the topic 'Quaternions algebra'

Author: Grafiati
Published: 7 June 2025
Last updated: 2 August 2025

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1

P, Ward J. Quaternions and Cayley numbers: Algebra and applications. Kluwer Academic Publishers, 1997.

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2

Ward, J. P. Quaternions and Cayley Numbers: Algebra and Applications. Springer Netherlands, 1997.

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3

Conway, John Horton. On quaternions and octonions: Their geometry, arithmetic, and symmetry. AK Peters, 2003.

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4

Chuang, Chih-Yun. Brandt matrices and theta series over global function fields. American Mathematical Society, 2015.

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5

Behrns, Vernon N. An introduction to the algebra of hypernumbers. Dorrance Publishing Co., 2007.

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6

Paşa, Hüseyin Tevfik. Hüseyin Tevfik Paşa ve "Linear algebra". İstanbul Teknik Üniversitesi Bilim ve Teknoloji Tarihi Araştırma Merkezi, 1988.

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7

Dixon, Geoffrey M. Division algebras: Octonions, quaternions, complex numbers, and the algebraic design of physics. Kluwer Academic Publishers, 1994.

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8

Voight, John. Quaternion Algebras. Springer International Publishing, 2021. http://dx.doi.org/10.1007/978-3-030-56694-4.

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9

Wolfgang, Sprössig, Gürlebeck Klaus, and Volkswagenstiftung, eds. Proceedings of the symposium: Analytical and numerical methods in quaternionic and Clifford analysis : Seiffen 1996. s.n., 1996.

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10

Fragoulopoulou, Maria. Tensor products of enveloping locally C*-algebras. Mathematisches Institut der Universität Münster, 1997.

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11

Hitzer, Eckhard. Quaternion and Clifford Fourier Transforms and Wavelets. Springer Basel, 2013.

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12

Chia-Hsiung, Tze, ed. On the role of division, Jordan, and related algebras in particle physics. World Scientific, 1996.

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13

Wolfgang, Sprössig, ed. Quaternionic and Clifford calculus for physicists and engineers. Wiley, 1997.

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14

Wiesław, Królikowski, ed. On Clifford-type structures. Institute of Mathematics, Polish Academy of Sciences, 2006.

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15

author, Tkachev Vladimir 1963, and Vlăduț, S. G. (Serge G.), 1954- author, eds. Nonlinear elliptic equations and nonassociative algebras. American Mathematical Society, 2014.

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16

Smith, Derek A., and John Horton Conway. On Quaternions and Octonions. CRC Press LLC, 2003.

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17

Smith, Derek A., and John Horton Conway. On Quaternions and Octonions. CRC Press LLC, 2003.

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18

Smith, Derek A., and John Horton Conway. On Quaternions and Octonions. CRC Press LLC, 2003.

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19

Smith, Derek A., and John Horton Conway. On Quaternions and Octonions. CRC Press LLC, 2003.

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20

Conway, John Horton, and Derek Smith. On Quaternions and Octonions. AK Peters, 2003.

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21

Girard, Patrick R. Quaternions, Clifford Algebras and Relativistic Physics. Birkhauser Verlag, 2007.

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22

Rodman, Leiba. Topics in Quaternion Linear Algebra. Princeton University Press, 2014.

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23

Rodman, Leiba. Topics in Quaternion Linear Algebra. Princeton University Press, 2014.

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24

Rodman, Leiba. Topics in Quaternion Linear Algebra. Princeton University Press, 2014.

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25

Snaith, Victor, Jeff Hooper, and Minh Van Tran. The Second Chinburg Conjecture for Quaternion Fields (Memoirs of the American Mathematical Society). American Mathematical Society, 2000.

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26

Roberts, Brooks Keiluweit. Lifting of automorphic forms on the units of a quaternion algebra to automorphic forms on the symplectic groups. 1992.

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27

Understanding geometric algebra: Hamilton, Grassmann, and Clifford for computer vision and graphics. CRC Press, 2015.

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28

M¨uhlherr, Bernhard, Holger P. Petersson, and Richard M. Weiss. Existence. Princeton University Press, 2017. http://dx.doi.org/10.23943/princeton/9780691166902.003.0016.

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This chapter proves that Bruhat-Tits buildings exist. It begins with a few definitions and simple observations about quadratic forms, including a 1-fold Pfister form, followed by a discussion of the existence part of the Structure Theorem for complete discretely valued fields due to H. Hasse and F. K. Schmidt. It then considers the generic unramified cases; the generic semi-ramified cases, the generic ramified cases, the wild unramified cases, the wild semi-ramified cases, and the wild ramified cases. These cases range from a unique unramified quadratic space to an unramified separable quadrat
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29

Voight, John. Quaternion Algebras. Springer International Publishing AG, 2021.

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30

Voight, John. Quaternion Algebras. Springer International Publishing AG, 2022.

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31

Quaternion Algebras. 2021.

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32

M¨uhlherr, Bernhard, Holger P. Petersson, and Richard M. Weiss. Linked Tori, II. Princeton University Press, 2017. http://dx.doi.org/10.23943/princeton/9780691166902.003.0006.

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This chapter proves several more results about weak isomorphisms between Moufang sets arising from quadratic forms and involutory sets. It first fixes a non-trivial anisotropic quadratic space Λ‎ = (K, L, q) before considering two proper anisotropic pseudo-quadratic spaces. It then describes a quaternion division algebra and its standard involution, a second quaternion division algebra and its standard involution, and an involutory set with a quaternion division algebra and its standard involution. It concludes with one more small observation regarding a pointed anisotropic quadratic space and
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33

M¨uhlherr, Bernhard, Holger P. Petersson, and Richard M. Weiss. Linked Tori, I. Princeton University Press, 2017. http://dx.doi.org/10.23943/princeton/9780691166902.003.0005.

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This chapter investigates the consequences of the assumption that one Moufang set is weakly isomorphic to another. It first introduces some well-known facts about involutions which are assembled in a few lemmas, including those dealing with an involutory set, a biquaternion division algebra, and a quaternion division algebra with a standard involution. It then presents a notation for a non-trivial anisotropic quadratic space and another for an involutory set are presented, along with assumptions for a pointed anisotropic quadratic space and the standard involution of a quaternion. It also make
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34

Quaternions, Clifford Algebras and Relativistic Physics. Birkhäuser Basel, 2007. http://dx.doi.org/10.1007/978-3-7643-7791-5.

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35

Quaternions, Clifford Algebras and Relativistic Physics. Birkhäuser Basel, 2007.

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36

Vigneras, M. F. Arithmetique des Algebres de Quaternions. Springer London, Limited, 2006.

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37

Quaternions as the result of algebraic operations. D. Van Nostrand company, 1990.

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38

M¨uhlherr, Bernhard, Holger P. Petersson, and Richard M. Weiss. Residually Pseudo-Split Buildings. Princeton University Press, 2017. http://dx.doi.org/10.23943/princeton/9780691166902.003.0033.

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This chapter presents results about a residually pseudo-split Bruhat-Tits building Ξ‎L. It begins with a case for some quadratic space of type E⁶, E₇, and E₈ in order to identify an unramified extension such that the residue field is a pseudo-splitting field. It then considers a wild quaternion or octonion division algebra and the existence of an unramified quadratic extension L/K such that L is a splitting field of the quaternion division algebra. It also discusses the properties of an unramified extension L/K and shows that every exceptional Bruhat-Tits building is the fixed point building o
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39

Dixon, G. M. Division Algebras : : Octonions Quaternions Complex Numbers and the Algebraic Design of Physics. Springer, 2013.

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40

Dual Quaternions and Their Associated Clifford Algebras. CRC Press LLC, 2023.

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41

Dual Quaternions and Their Associated Clifford Algebras. Taylor & Francis Group, 2023.

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42

M¨uhlherr, Bernhard, Holger P. Petersson, and Richard M. Weiss. Quadratic Forms of Type E6, E7 and E8. Princeton University Press, 2017. http://dx.doi.org/10.23943/princeton/9780691166902.003.0008.

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This chapter presents various results about quadratic forms of type E⁶, E₇, and E₈. It first recalls the definition of a quadratic space Λ‎ = (K, L, q) of type Eℓ for ℓ = 6, 7 or 8. If D₁, D₂, and D₃ are division algebras, a quadratic form of type E⁶ can be characterized as the anisotropic sum of two quadratic forms, one similar to the norm of a quaternion division algebra D over K and the other similar to the norm of a separable quadratic extension E/K such that E is a subalgebra of D over K. Also, there exist fields of arbitrary characteristic over which there exist quadratic forms of type E
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43

Invariant Theory of Matrices. American Mathematical Society, 2017.

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44

Baker, Arthur Latham. Quaternions As the Result of Algebraic Operations. Creative Media Partners, LLC, 2018.

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45

Quaternions as the Result of Algebraic Operations. Franklin Classics, 2018.

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46

Baker, Arthur Latham. Quaternions as the Result of Algebraic Operations. Franklin Classics Trade Press, 2018.

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47

Baker, Arthur Latham. Quaternions As The Result Of Algebraic Operations. Franklin Classics, 2018.

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48

Baker, Arthur Latham. Quaternions as the Result of Algebraic Operations. Andesite Press, 2017.

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49

Quaternions As The Result Of Algebraic Operations. Franklin Classics, 2018.

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50

Baker, Arthur Latham. Quaternions As the Result of Algebraic Operations. Creative Media Partners, LLC, 2022.

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