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Mathematics Subject Classification – MSC2010

17-XX

Nonassociative rings and algebras 41023

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) 484

17-03

Historical (must also be assigned at least one classification number from Section 01) 67

17-04

Explicit machine computation and programs (not the theory of computation or programming) 126

17-06

Proceedings, conferences, collections, etc. 475

17-08

Computational methods 223

17Axx

General nonassociative rings 6111

17A01

General theory 178

17A05

Power-associative rings 238

17A15

Noncommutative Jordan algebras 159

17A20

Flexible algebras 151

17A30

Algebras satisfying other identities 1208

17A32

Leibniz algebras 485

17A35

Division algebras 485

17A36

Automorphisms, derivations, other operators 400

17A40

Ternary compositions 770

17A42

Other $n$-ary compositions (n \ge 3)$ 317

17A45

Quadratic algebras (but not quadratic Jordan algebras) 134

Free algebras 259

Structure theory 389

Radical theory 235

Superalgebras 1344

Composition algebras 278

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] 33062

17B01

Identities, free Lie (super)algebras 954

17B05

Structure theory 1697

17B08

Coadjoint orbits; nilpotent varieties 268

17B10

Representations, algebraic theory (weights) 4291

17B15

Representations, analytic theory 302

17B20

Simple, semisimple, reductive (super)algebras 2947

17B22

Root systems 421

17B25

Exceptional (super)algebras 416

17B30

Solvable, nilpotent (super)algebras 2224

17B35

Universal enveloping (super)algebras [See also 16S30] 1911

17B37

Quantum groups (quantized enveloping algebras) and related deformations [See also 16T20, 20G42, 81R50, 82B23] 7849

17B40

Automorphisms, derivations, other operators 1522

17B45

Lie algebras of linear algebraic groups [See also 14Lxx and 20Gxx] 855

17B50

Modular Lie (super)algebras 1339

17B55

Homological methods in Lie (super)algebras 843

17B56

Cohomology of Lie (super)algebras 1760

17B60

Lie (super)algebras associated with other structures (associative, Jordan, etc.) [See also 16W10, 17C40, 17C50] 1010

17B62

Lie bialgebras; Lie coalgebras 376

17B63

Poisson algebras 714

17B65

Infinite-dimensional Lie (super)algebras [See also 22E65] 2422

17B66

Lie algebras of vector fields and related (super) algebras 1023

17B67

Kac-Moody (super)algebras; extended affine Lie algebras; toroidal Lie algebras 3015

17B68

Virasoro and related algebras 1753

17B69

Vertex operators; vertex operator algebras and related structures 1596

17B70

Graded Lie (super)algebras 1924

17B75

Color Lie (super)algebras 121

17B80

Applications to integrable systems 612

17B81

Applications to physics 1866

17B99

None of the above, but in this section 1070

17Cxx

Jordan algebras (algebras, triples and pairs) 2573

17C05

Identities and free Jordan structures 201

17C10

Structure theory 587

17C17

Radicals 39

17C20

Simple, semisimple algebras 268

17C27

Idempotents, Peirce decompositions 81

17C30

Associated groups, automorphisms 133

17C36

Associated manifolds 45

17C37

Associated geometries 47

17C40

Exceptional Jordan structures 149

17C50

Jordan structures associated with other structures [See also 16W10] 508

17C55

Finite-dimensional structures 103

17C60

Division algebras 42

17C65

Jordan structures on Banach spaces and algebras [See also 46H70, 46L70] 640

17C70

Super structures 165

17C90

Applications to physics 36

17C99

None of the above, but in this section 204

17Dxx

Other nonassociative rings and algebras 2373

17D05

Alternative rings 872

17D10

Mal’cev (Mal’tsev) rings and algebras 275

17D15

Right alternative rings 140

17D20

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

17D25

Lie-admissible algebras 254

17D92

Genetic algebras 416

17D99

None of the above, but in this section 553

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Mathematics Subject Classification – MSC2010

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