000 05809nam a2200721 i 4500
001 9780750326483
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006 m eo d
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008 220705s2022 enka fob 000 0 eng d
020 _a9780750326483
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020 _a9780750326476
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020 _z9780750326469
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020 _z9780750326490
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024 7 _a10.1088/978-0-7503-2648-3
_2doi
035 _a(CaBNVSL)thg00083288
035 _a(OCoLC)1336503003
040 _aCaBNVSL
_beng
_erda
_cCaBNVSL
_dCaBNVSL
050 4 _aQA162
_b.D877 2022eb
072 7 _aPBU
_2bicssc
072 7 _aMAT002010
_2bisacsh
082 0 4 _a512/.02
_223
100 1 _aDupli�i, Stepan,
_eauthor.
_970738
245 1 0 _aPolyadic algebraic structures /
_cSteven Duplij.
264 1 _aBristol [England] (Temple Circus, Temple Way, Bristol BS1 6HG, UK) :
_bIOP Publishing,
_c[2022]
300 _a1 online resource (various pagings) :
_billustrations.
336 _atext
_2rdacontent
337 _aelectronic
_2isbdmedia
338 _aonline resource
_2rdacarrier
490 1 _a[IOP release $release]
490 1 _aIOP ebooks. [2022 collection]
500 _a"Version: 20220601"--Title page verso.
504 _aIncludes bibliographical references.
505 0 _apart I. One-set polyadic algebraic structures. 1. One-set algebraic structures and Hossz�u-Gluskin theorem -- 1.1. General properties of one-set one-operation polyadic structures -- 1.2. Polyadic semigroups, quasigroups and groups -- 1.3. Polyadic direct products and changed arity powers -- 1.4. The deformed Hossz�u-Gluskin theorem -- 1.5. Polyadic analog of Grothendieck group
505 8 _a2. Representations and heteromorphisms -- 2.1. Homomorphisms of one-set polyadic algebraic structures -- 2.2. Heteromorphisms of one-set polyadic algebraic structures -- 2.3. Hetero-covering of algebraic structures -- 2.4. Multiplace representations of polyadic algebraic structures -- 2.5. k-Place actions
505 8 _a3. Polyadic semigroups and higher regularity -- 3.1. Generalized q-regular elements in semigroups -- 3.2. Higher q-inverse semigroups -- 3.3. Higher q-inverse polyadic semigroups -- 3.4. Polyadic-binary correspondence, regular semigroups, braid groups
505 8 _a4. Polyadic rings, fields and integer numbers -- 4.1. One-set polyadic 'linear' structures -- 4.2. Polyadic direct products of rings and fields -- 4.3. Polyadic integer numbers -- 4.4. Finite polyadic rings of integers -- 4.5. Finite polyadic fields of integer numbers -- 4.6. Diophantine equations over polyadic integers and Fermat's theorem
505 8 _apart II. Two-sets polyadic algebraic structures. 5. Polyadic algebras and deformations -- 5.1. Two-set polyadic structures -- 5.2. Mappings between polyadic vector spaces -- 5.3. Polyadic associative algebras
505 8 _a6. Polyadic inner spaces and operators -- 6.1. Polyadic inner pairing spaces and norms -- 6.2. Elements of polyadic operator theory
505 8 _a7. Medial deformation of n-ary algebras -- 7.1. Almost commutative graded algebra -- 7.2. Almost medial graded algebras -- 7.3. Medial n-ary algebras -- 7.4. Almost medial n-ary graded algebras -- 7.5. Toyoda's theorem for almost medial algebras
505 8 _a8. Membership deformations and obscure n-ary algebras -- 8.1. Graded algebras and Shur factors -- 8.2. Membership function and obscure algebras -- 8.3. Membership deformation of commutativity -- 8.4. Projective representations -- 8.5. n-ary double commutative algebras -- 8.6. Conclusions
505 8 _apart III. Polyadic quantum groups. 9. Polyadic Hopf algebras -- 9.1. Polyadic coalgebras -- 9.2. Polyadic bialgebras -- 9.3. Polyadic Hopf algebras -- 9.4. Ternary examples -- 9.5. Polyadic almost co-commutativity and co-mediality
505 8 _a10. Solutions to higher braid equations -- 10.1. Yang-Baxter operators -- 10.2. Polyadic braid operators and higher braid equations -- 10.3. Solutions to the ternary braid equations
505 8 _apart IV. Polyadic categories. 11. Polyadic tensor categories -- 11.1. Binary tensor categories -- 11.2. Polyadic tensor categories -- 11.3. Polyadic units, unitors and quertors -- 11.4. Braided tensor categories -- 11.5. Medialed polyadic tensor categories -- 11.6. Conclusions.
520 3 _aThe book is devoted to the thorough study of polyadic (higher arity) algebraic structures, which has a long history, starting from 19th century.
521 _aComputational physics, theoretical physics, mathematicians.
530 _aAlso available in print.
538 _aMode of access: World Wide Web.
538 _aSystem requirements: Adobe Acrobat Reader, EPUB reader, or Kindle reader.
545 _aSteven Duplij (Stepan Douplii) is a theoretical and mathematical physicist from the University of M�unster, Germany. Dr. Duplij is the editor-compiler of 'Concise Encyclopaedia of Supersymmetry' (2005, Springer), and is the author of more than a hundred scientific publications and several books. His scientific directions include supersymmetry and quantum groups, advanced algebraic structures, gravity and nonlinear electrodynamics, constrained systems and quantum computing.
588 0 _aTitle from PDF title page (viewed on July 5, 2022).
650 0 _aAlgebra, Abstract.
_920960
650 0 _aPolyadic algebras.
_970739
650 7 _aOptimization.
_2bicssc
_970740
650 7 _aMathematics and computation.
_2bisacsh
_970439
710 2 _aInstitute of Physics (Great Britain),
_epublisher.
_911622
776 0 8 _iPrint version:
_z9780750326469
_z9780750326490
830 0 _aIOP (Series).
_pRelease 22.
_970741
830 0 _aIOP ebooks.
_p2022 collection.
_970742
856 4 0 _uhttps://iopscience.iop.org/book/978-0-7503-2648-3
942 _cEBK
999 _c82897
_d82897