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Mathematics Subject Classification – MSC2010

17-XX

Nonassociative rings and algebras 39991

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) 473

17-03

Historical (must also be assigned at least one classification number from Section 01) 64

17-04

Explicit machine computation and programs (not the theory of computation or programming) 123

17-06

Proceedings, conferences, collections, etc. 464

17-08

Computational methods 222

17Axx

General nonassociative rings 5958

17A01

General theory 169

17A05

Power-associative rings 227

17A15

Noncommutative Jordan algebras 159

17A20

Flexible algebras 150

17A30

Algebras satisfying other identities 1179

17A32

Leibniz algebras 452

17A35

Division algebras 470

17A36

Automorphisms, derivations, other operators 383

17A40

Ternary compositions 749

17A42

Other $n$-ary compositions (n \ge 3)$ 308

17A45

Quadratic algebras (but not quadratic Jordan algebras) 131

Free algebras 250

Structure theory 365

Radical theory 231

Superalgebras 1329

Composition algebras 269

17A80

Valued algebras 68

17A99

None of the above, but in this section 393

17Bxx

Lie algebras and Lie superalgebras [For Lie groups, see 22Exx] 32193

17B01

Identities, free Lie (super)algebras 930

17B05

Structure theory 1659

17B08

Coadjoint orbits; nilpotent varieties 246

17B10

Representations, algebraic theory (weights) 4166

17B15

Representations, analytic theory 301

17B20

Simple, semisimple, reductive (super)algebras 2858

17B22

Root systems 381

17B25

Exceptional (super)algebras 401

17B30

Solvable, nilpotent (super)algebras 2166

17B35

Universal enveloping (super)algebras [See also 16S30] 1876

17B37

Quantum groups (quantized enveloping algebras) and related deformations [See also 16T20, 20G42, 81R50, 82B23] 7694

17B40

Automorphisms, derivations, other operators 1463

17B45

Lie algebras of linear algebraic groups [See also 14Lxx and 20Gxx] 835

17B50

Modular Lie (super)algebras 1315

17B55

Homological methods in Lie (super)algebras 827

17B56

Cohomology of Lie (super)algebras 1719

17B60

Lie (super)algebras associated with other structures (associative, Jordan, etc.) [See also 16W10, 17C40, 17C50] 978

17B62

Lie bialgebras; Lie coalgebras 354

17B63

Poisson algebras 670

17B65

Infinite-dimensional Lie (super)algebras [See also 22E65] 2392

17B66

Lie algebras of vector fields and related (super) algebras 995

17B67

Kac-Moody (super)algebras; extended affine Lie algebras; toroidal Lie algebras 2904

17B68

Virasoro and related algebras 1704

17B69

Vertex operators; vertex operator algebras and related structures 1515

17B70

Graded Lie (super)algebras 1890

17B75

Color Lie (super)algebras 111

17B80

Applications to integrable systems 568

17B81

Applications to physics 1811

17B99

None of the above, but in this section 1056

17Cxx

Jordan algebras (algebras, triples and pairs) 2528

17C05

Identities and free Jordan structures 196

17C10

Structure theory 578

17C17

Radicals 37

17C20

Simple, semisimple algebras 260

17C27

Idempotents, Peirce decompositions 76

17C30

Associated groups, automorphisms 129

17C36

Associated manifolds 45

17C37

Associated geometries 45

17C40

Exceptional Jordan structures 148

17C50

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

17C55

Finite-dimensional structures 97

17C60

Division algebras 41

17C65

Jordan structures on Banach spaces and algebras [See also 46H70, 46L70] 628

17C70

Super structures 160

17C90

Applications to physics 36

17C99

None of the above, but in this section 203

17Dxx

Other nonassociative rings and algebras 2326

17D05

Alternative rings 864

17D10

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

17D15

Right alternative rings 138

17D20

(\gamma, \delta)$-rings, including $(1,-1)$-rings 88

17D25

Lie-admissible algebras 240

17D92

Genetic algebras 410

17D99

None of the above, but in this section 539

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Mathematics Subject Classification – MSC2010

Overview