zbMATH — the first resource for mathematics

Mathematics Subject Classification – MSC2010

17-XX

Nonassociative rings and algebras 40263

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) 476

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. 468

17-08

Computational methods 223

17Axx

General nonassociative rings 6007

17A01

General theory 174

17A05

Power-associative rings 229

17A15

Noncommutative Jordan algebras 160

17A20

Flexible algebras 150

17A30

Algebras satisfying other identities 1187

17A32

Leibniz algebras 462

17A35

Division algebras 476

17A36

Automorphisms, derivations, other operators 387

17A40

Ternary compositions 756

17A42

Other $n$-ary compositions (n \ge 3)$ 310

17A45

Quadratic algebras (but not quadratic Jordan algebras) 132

Free algebras 251

Structure theory 375

Radical theory 232

Superalgebras 1334

Composition algebras 272

17A80

Valued algebras 68

17A99

None of the above, but in this section 395

17Bxx

Lie algebras and Lie superalgebras [For Lie groups, see 22Exx] 32410

17B01

Identities, free Lie (super)algebras 936

17B05

Structure theory 1666

17B08

Coadjoint orbits; nilpotent varieties 251

17B10

Representations, algebraic theory (weights) 4193

17B15

Representations, analytic theory 301

17B20

Simple, semisimple, reductive (super)algebras 2882

17B22

Root systems 388

17B25

Exceptional (super)algebras 402

17B30

Solvable, nilpotent (super)algebras 2182

17B35

Universal enveloping (super)algebras [See also 16S30] 1884

17B37

Quantum groups (quantized enveloping algebras) and related deformations [See also 16T20, 20G42, 81R50, 82B23] 7737

17B40

Automorphisms, derivations, other operators 1480

17B45

Lie algebras of linear algebraic groups [See also 14Lxx and 20Gxx] 838

17B50

Modular Lie (super)algebras 1319

17B55

Homological methods in Lie (super)algebras 832

17B56

Cohomology of Lie (super)algebras 1728

17B60

Lie (super)algebras associated with other structures (associative, Jordan, etc.) [See also 16W10, 17C40, 17C50] 990

17B62

Lie bialgebras; Lie coalgebras 358

17B63

Poisson algebras 681

17B65

Infinite-dimensional Lie (super)algebras [See also 22E65] 2407

17B66

Lie algebras of vector fields and related (super) algebras 1000

17B67

Kac-Moody (super)algebras; extended affine Lie algebras; toroidal Lie algebras 2927

17B68

Virasoro and related algebras 1723

17B69

Vertex operators; vertex operator algebras and related structures 1535

17B70

Graded Lie (super)algebras 1907

17B75

Color Lie (super)algebras 114

17B80

Applications to integrable systems 577

17B81

Applications to physics 1826

17B99

None of the above, but in this section 1058

17Cxx

Jordan algebras (algebras, triples and pairs) 2540

17C05

Identities and free Jordan structures 196

17C10

Structure theory 583

17C17

Radicals 38

17C20

Simple, semisimple algebras 263

17C27

Idempotents, Peirce decompositions 78

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] 501

17C55

Finite-dimensional structures 98

17C60

Division algebras 43

17C65

Jordan structures on Banach spaces and algebras [See also 46H70, 46L70] 630

17C70

Super structures 163

17C90

Applications to physics 36

17C99

None of the above, but in this section 203

17Dxx

Other nonassociative rings and algebras 2336

17D05

Alternative rings 864

17D10

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

17D15

Right alternative rings 139

17D20

(\gamma, \delta)$-rings, including $(1,-1)$-rings 89

17D25

Lie-admissible algebras 241

17D92

Genetic algebras 415

17D99

None of the above, but in this section 542

Overview

General mathematics

History and biography

Mathematical logic and foundations

Combinatorics

Order, lattices, ordered algebraic structures

General algebraic systems

Number theory

Field theory and polynomials

Commutative algebra

Algebraic geometry

Linear and multilinear algebra; matrix theory

Associative rings and algebras

Nonassociative rings and algebras

Category theory, homological algebra

$K$-theory

Group theory and generalizations

Topological groups, Lie groups

Real functions

Measure and integration

Functions of a complex variable

Potential theory

Several complex variables and analytic spaces

Special functions

Ordinary differential equations

Partial differential equations

Dynamical systems and ergodic theory

Difference and functional equations

Sequences, series, summability

Approximation and expansions

Harmonic analysis on Euclidean spaces

Abstract harmonic analysis

Integral transforms, operational calculus

Integral equations

Functional analysis

Operator theory

Calculus of variations and optimal control; optimization

Geometry

Convex and discrete geometry

Differential geometry

General topology

Algebraic topology

Manifolds and cell complexes

Global analysis, analysis on manifolds

Probability theory and stochastic processes

Statistics

Numerical analysis

Computer science

Mechanics of particles and systems

Mechanics of deformable solids

Fluid mechanics

Optics, electromagnetic theory

Classical thermodynamics, heat transfer

Quantum Theory

Statistical mechanics, structure of matter

Relativity and gravitational theory

Astronomy and astrophysics

Geophysics

Operations research, mathematical programming

Game theory, economics, social and behavioral sciences

Biology and other natural sciences

Systems theory; control

Information and communication, circuits

Mathematics education

any	anywhere
cc	classification code
ct	classification text

a & b	logic and	abc*	right wildcard
a \| b	logic or	"ab c"	phrase
!ab	logic not	(ab c)	parentheses

zbMATH — the first resource for mathematics

Examples

Fields

Operators

Mathematics Subject Classification – MSC2010

Overview