Mathematics Mathematical objects

Mathematical objects

Real Lie algebras
Table legend:S: Is this algebra simple? (Yes or No)SS: Is this algebra semi-simple? (Yes or No)Lie algebra Description S SS Remarks dim/RR the real numbers, the Lie bracket is zero 1Rn the Lie brac ...
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Real Lie groups and their algebras
Column legendCM: Is this group G compact? (Yes or No)\pi_0: Gives the group of components of G. The order of the component group gives the number of connected components. The group is connected if and ...
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Table of Lie groups
This article gives a table of some common Lie groups and their associated Lie algebras.The following are noted: the topological properties of the group (dimension; connectedness; compactness; the natu ...
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List of surfaces
Minimal surfacesCatalan's minimal surfaceCosta surfaceCatenoidEnneper surfaceGyroidHelicoidLidinoidRiemann's minimal surfaceSaddle towerScherk surfaceSchwarz minimal surfaceTriply periodic minimal sur ...
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List of complex and algebraic surfaces
Algebraic and complex surfacesabelian surfaces (κ = 0) Two-dimensional abelian varieties.algebraic surfacesBarlow surfaces General type, simply connected.Barth surfaces Surfaces of degrees 6 and 10 w ...
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List of special functions and eponyms
ANiels Abel: Abel polynomials - Abelian function - Abel–Gontscharoff interpolating polynomialSir George Biddell Airy: Airy functionWaleed Al-Salam (1926–1996): Al-Salam polynomial - Al Salam–Carlit ...
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Zn: the cyclic group of order n (the notation Cn is also used; it is isomorphic to the additive group of Z/nZ).Dihn: the dihedral group of order 2n (often the notation Dn or D2n is used )Sn: the symme ...
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List of small groups
The list can be used to determine which known group a given finite group G is isomorphic to: first determine the order of G, then look up the candidates for that order in the list below. If you know w ...
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List of simple Lie groups
Simple Lie groupsUnfortunately, there is no generally accepted definition of a simple Lie group. In particular, it is not necessarily defined as a Lie group that is simple as an abstract group. Author ...
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An apeirotope is, like any other polytope, an unbounded hyper-surface. The difference is that whereas a polytope's hyper-surface curls back on itself to close round a finite volume of hyperspace, an a ...
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Two-dimensional regular polytopes
The two-dimensional polytopes are called polygons. Regular polygons are equilateral and cyclic. A p-gonal regular polygon is represented by Schläfli symbol {p}.Usually only convex polygons are consid ...
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This table shows a summary of regular polytope counts by dimension.Dimension Convex Nonconvex ConvexEuclideantessellations Convexhyperbolictessellations Nonconvexhyperbolictessellations Hyperbolic Tes ...
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List of regular polytopes
This page lists the regular polytopes in Euclidean, spherical and hyperbolic spaces. The Schläfli symbol notation describes every regular polytope, and is used widely below as a compact reference nam ...
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Geometric operators
Rectification (geometry)Truncation (geometry)BitruncationCantellationRuncinationStericationOmnitruncationExpansion (geometry)Snub (geometry)Alternation (geometry)Dual polyhedronGyration (geometry)Elon ...
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Dimensional families
Regular polytope and List of regular polytopesSimplexHypercubeCross-polytopeUniform polytopeDemihypercubeUniform 1k2 polytopeUniform 2k1 polytopeUniform k21 polytopeHoneycombsHypercubic honeycombAlter ...
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