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Mathematics Subject Classification – MSC2010

17-XX

Nonassociative rings and algebras 40624

17-00

General reference works (handbooks, dictionaries, bibliographies, etc.) 9

17-01

Instructional exposition (textbooks, tutorial papers, etc.) 163

17-02

Research exposition (monographs, survey articles) 479

17-03

Historical (must also be assigned at least one classification number from Section 01) 65

17-04

Explicit machine computation and programs (not the theory of computation or programming) 124

17-06

Proceedings, conferences, collections, etc. 472

17-08

Computational methods 224

17Axx

General nonassociative rings 6057

17A01

General theory 176

17A05

Power-associative rings 232

17A15

Noncommutative Jordan algebras 162

17A20

Flexible algebras 151

17A30

Algebras satisfying other identities 1196

17A32

Leibniz algebras 471

17A35

Division algebras 484

17A36

Automorphisms, derivations, other operators 392

17A40

Ternary compositions 767

17A42

Other $n$-ary compositions (n \ge 3)$ 311

17A45

Quadratic algebras (but not quadratic Jordan algebras) 133

Free algebras 256

Structure theory 380

Radical theory 234

Superalgebras 1333

Composition algebras 276

17A80

Valued algebras 69

17A99

None of the above, but in this section 392

17Bxx

Lie algebras and Lie superalgebras [For Lie groups, see 22Exx] 32751

17B01

Identities, free Lie (super)algebras 945

17B05

Structure theory 1682

17B08

Coadjoint orbits; nilpotent varieties 260

17B10

Representations, algebraic theory (weights) 4242

17B15

Representations, analytic theory 302

17B20

Simple, semisimple, reductive (super)algebras 2914

17B22

Root systems 408

17B25

Exceptional (super)algebras 408

17B30

Solvable, nilpotent (super)algebras 2207

17B35

Universal enveloping (super)algebras [See also 16S30] 1899

17B37

Quantum groups (quantized enveloping algebras) and related deformations [See also 16T20, 20G42, 81R50, 82B23] 7796

17B40

Automorphisms, derivations, other operators 1508

17B45

Lie algebras of linear algebraic groups [See also 14Lxx and 20Gxx] 846

17B50

Modular Lie (super)algebras 1324

17B55

Homological methods in Lie (super)algebras 833

17B56

Cohomology of Lie (super)algebras 1748

17B60

Lie (super)algebras associated with other structures (associative, Jordan, etc.) [See also 16W10, 17C40, 17C50] 997

17B62

Lie bialgebras; Lie coalgebras 365

17B63

Poisson algebras 697

17B65

Infinite-dimensional Lie (super)algebras [See also 22E65] 2413

17B66

Lie algebras of vector fields and related (super) algebras 1012

17B67

Kac-Moody (super)algebras; extended affine Lie algebras; toroidal Lie algebras 2985

17B68

Virasoro and related algebras 1743

17B69

Vertex operators; vertex operator algebras and related structures 1567

17B70

Graded Lie (super)algebras 1917

17B75

Color Lie (super)algebras 117

17B80

Applications to integrable systems 599

17B81

Applications to physics 1844

17B99

None of the above, but in this section 1067

17Cxx

Jordan algebras (algebras, triples and pairs) 2559

17C05

Identities and free Jordan structures 198

17C10

Structure theory 584

17C17

Radicals 38

17C20

Simple, semisimple algebras 268

17C27

Idempotents, Peirce decompositions 79

17C30

Associated groups, automorphisms 132

17C36

Associated manifolds 45

17C37

Associated geometries 46

17C40

Exceptional Jordan structures 149

17C50

Jordan structures associated with other structures [See also 16W10] 502

17C55

Finite-dimensional structures 101

17C60

Division algebras 42

17C65

Jordan structures on Banach spaces and algebras [See also 46H70, 46L70] 638

17C70

Super structures 164

17C90

Applications to physics 36

17C99

None of the above, but in this section 202

17Dxx

Other nonassociative rings and algebras 2356

17D05

Alternative rings 869

17D10

Mal’cev (Mal’tsev) rings and algebras 274

17D15

Right alternative rings 139

17D20

(\gamma, \delta)$-rings, including $(1,-1)$-rings 91

17D25

Lie-admissible algebras 248

17D92

Genetic algebras 415

17D99

None of the above, but in this section 548

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Mathematics Subject Classification – MSC2010

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