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Mathematics Subject Classification – MSC2010

17-XX

Nonassociative rings and algebras 40454

17-00

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

17-01

Instructional exposition (textbooks, tutorial papers, etc.) 164

17-02

Research exposition (monographs, survey articles) 478

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. 469

17-08

Computational methods 224

17Axx

General nonassociative rings 6038

17A01

General theory 174

17A05

Power-associative rings 231

17A15

Noncommutative Jordan algebras 162

17A20

Flexible algebras 150

17A30

Algebras satisfying other identities 1189

17A32

Leibniz algebras 470

17A35

Division algebras 481

17A36

Automorphisms, derivations, other operators 390

17A40

Ternary compositions 763

17A42

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

17A45

Quadratic algebras (but not quadratic Jordan algebras) 133

Free algebras 253

Structure theory 375

Radical theory 234

Superalgebras 1337

Composition algebras 274

17A80

Valued algebras 69

17A99

None of the above, but in this section 393

17Bxx

Lie algebras and Lie superalgebras [For Lie groups, see 22Exx] 32570

17B01

Identities, free Lie (super)algebras 937

17B05

Structure theory 1675

17B08

Coadjoint orbits; nilpotent varieties 255

17B10

Representations, algebraic theory (weights) 4216

17B15

Representations, analytic theory 301

17B20

Simple, semisimple, reductive (super)algebras 2893

17B22

Root systems 395

17B25

Exceptional (super)algebras 405

17B30

Solvable, nilpotent (super)algebras 2194

17B35

Universal enveloping (super)algebras [See also 16S30] 1887

17B37

Quantum groups (quantized enveloping algebras) and related deformations [See also 16T20, 20G42, 81R50, 82B23] 7775

17B40

Automorphisms, derivations, other operators 1493

17B45

Lie algebras of linear algebraic groups [See also 14Lxx and 20Gxx] 843

17B50

Modular Lie (super)algebras 1326

17B55

Homological methods in Lie (super)algebras 833

17B56

Cohomology of Lie (super)algebras 1737

17B60

Lie (super)algebras associated with other structures (associative, Jordan, etc.) [See also 16W10, 17C40, 17C50] 991

17B62

Lie bialgebras; Lie coalgebras 359

17B63

Poisson algebras 688

17B65

Infinite-dimensional Lie (super)algebras [See also 22E65] 2408

17B66

Lie algebras of vector fields and related (super) algebras 1007

17B67

Kac-Moody (super)algebras; extended affine Lie algebras; toroidal Lie algebras 2945

17B68

Virasoro and related algebras 1732

17B69

Vertex operators; vertex operator algebras and related structures 1546

17B70

Graded Lie (super)algebras 1912

17B75

Color Lie (super)algebras 114

17B80

Applications to integrable systems 587

17B81

Applications to physics 1833

17B99

None of the above, but in this section 1061

17Cxx

Jordan algebras (algebras, triples and pairs) 2553

17C05

Identities and free Jordan structures 197

17C10

Structure theory 583

17C17

Radicals 38

17C20

Simple, semisimple algebras 264

17C27

Idempotents, Peirce decompositions 78

17C30

Associated groups, automorphisms 130

17C36

Associated manifolds 45

17C37

Associated geometries 45

17C40

Exceptional Jordan structures 149

17C50

Jordan structures associated with other structures [See also 16W10] 504

17C55

Finite-dimensional structures 101

17C60

Division algebras 42

17C65

Jordan structures on Banach spaces and algebras [See also 46H70, 46L70] 634

17C70

Super structures 163

17C90

Applications to physics 36

17C99

None of the above, but in this section 204

17Dxx

Other nonassociative rings and algebras 2341

17D05

Alternative rings 865

17D10

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

17D15

Right alternative rings 139

17D20

(\gamma, \delta)$-rings, including $(1,-1)$-rings 90

17D25

Lie-admissible algebras 241

17D92

Genetic algebras 415

17D99

None of the above, but in this section 545

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Mathematics Subject Classification – MSC2010

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