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(mathematics) A homomorphism that transforms a group into an abelian group.
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(linear algebra) A linear combination (of vectors in Euclidean space) in which the coefficients all add up to one.
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(differential geometry) A type of differential geometry in which the differential invariants studied are invariant under volume-preserving affine transformations.
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(algebraic geometry) A set of points (in n-dimensional space) which satisfy a set of equations which have a polynomial of n variables on one side and a zero on the other side.
adj
(mathematics) Describing algebraic characteristics of groupoids
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(graph theory) Clipping of graph antihole. [(mathematics) The complement of a graph hole]
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(mathematics) A negative 1-soliton solution to the Sine–Gordon equation
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(mathematics) A particular form of vector space that is a compatible form of two algebras.
adj
(mathematics) Hermitian in x for every y and hermitian in y for every x.
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(linear algebra) A function of two arguments from the same vector space which maps onto a field of scalars, which acts like a linear form with respect to either one of its arguments when the other one is held constant.
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(mathematics) The space, denoted by ℬ or ℬ, of holomorphic functions f defined on the open unit disc D in the complex plane, such that the function (1-|z|²)|f^′(z)| is bounded.
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(mathematics) Any of the scalar products a_ij=2(r_i,r_j)/(r_i,r_i) that make up the Cartan matrix of a simple Lie algebra.
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(mathematics) A construction that produces a sequence of Cayley-Dickson algebras: algebras over the field of real numbers, each with twice the dimension of the previous one.
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(mathematics) The dual of the area.
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(mathematics) The image of a submodule of a cochain
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(mathematics) The dual of a circuit.
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(mathematics) A 1-uniform morphism; an injective morphism; a morphism that maps letter to letter
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(mathematics) A particular form of mapping. A continuous mapping i:A→X, where A and X are topological spaces, is a cofibration if it satisfies the homotopy extension property with respect to all spaces Y.
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(mathematics) A method of contravariantly associating a family of invariant quotient groups to each algebraic or geometric object of a category, including categories of geometric and algebraic objects.
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(mathematics) The dual of a module.
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(mathematics) The transpose of a matrix, after replacing each element with its complex conjugate.
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(mathematics) The dimension of the cokernel of a linear transformation of a vector space
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(mathematics) The dual of a sheaf.
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(linear algebra) A scalar product.
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(algebra, of a sequence of groups connected by homomorphisms) Such that the kernel of one homomorphism is the image of the preceding one.
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A non-singular complete algebraic variety whose anticanonical bundle is ample.
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(mathematics) An abstract construction in homological algebra and geometry providing a certain type of generalisation for a sheaf.
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(geometry) A basic result in discrete geometry on the intersection of convex sets, which gave rise to the notion of a Helly family.
adj
(algebra, of a ring or field) Which satisfies the criteria for (some formulation of) Hensel's lemma.
adj
(mathematics) Of a ring: such that all submodules of projective modules over the ring are also projective.
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(mathematics) A real, multivariate homogeneous polynomial p(x) is hyperbolic (in direction e) if p(x-te) = 0 has only real roots as a function of t.
adj
(mathematics, of groups) Displaying a generalization of sofic that applies to finite-dimensional Hilbert spaces.
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(algebra) An operation on a group, analogous to negation.
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(mathematics) That commutes with the actions of a group on the domain and codomain, and preserves isotropy subgroups of elements that fix points in the domain and codomain.
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(mathematics) The second unit vector, after i
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(graph theory) A square n⨯n matrix which describes an undirected graph of n vertices by letting rows and columns correspond to vertices, letting its diagonal elements contain the degrees of corresponding vertices and letting its non-diagonal elements contain either −1 or 0 depending on whether there is or there is not (respectively) an edge connecting the pair of corresponding vertices.
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(linear algebra) A subset of vectors of a vector space which is closed under the addition and scalar multiplication of that vector space.
adj
(economics) Of a matrix, having negative elements on the main diagonal and non-negative elements everywhere else.
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(mathematics) The unexpected connection between the Monster group and modular functions, now known to relate to a certain conformal field theory having the Monster group as symmetries.
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(mathematics) An algebra composed of a set and a family of multioperations on that set
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(linear algebra, multilinear algebra) Given a vector space V over a field K of scalars, a mapping Vᵏ → K that is linear in each of its arguments;
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(mathematics) Related to a bicomplex value by a power of -1.
adj
(algebra) Of a module in which any ascending chain of submodules eventually starts repeating.
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(mathematics, physics) A version of C*-algebra which does away with commutativity, and the geometry which would be generated by/associated with such a modified algebra.
adj
This means that the vector space of solutions of (2.25) near 𝜆=0 is generated by
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(mathematical analysis) The endowing of a vector space, etc. with a norm.
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(mathematics) An extension of the paralinearization of non-smooth functions, used to flatten pairs of surfaces by changing variables.
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(mathematics) A sum (in some algebras) of a scalar and a vector.
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(algebra) A particular group theoretic operation on a set of functions of a given symmetry type.
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(mathematics) A generalization of a cover in which the kernal may contain a non-zero pure subgroup.
adj
(mathematics) Isomorphic to the limit of a filtered projective system of discrete groups.
adj
(mathematics) Describing certain topological groups formed from finite groups
adj
(group theory, of a subgroup) Such that each of its conjugates is conjugate to it already in the subgroup generated by it and its conjugate.
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(functional analysis) A generalization of the Pythagorean theorem for Euclidean triangles to Hilbert spaces
adj
(mathematics, of a group) Being a perfect central extension of a simple group S.
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(topology) A surjective, continuous function from one topological space to another one, such that the latter one's topology has the property that if the inverse image (under the said function) of some subset of it is open in the function's domain, then the subset is open in the target space.
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(linear algebra, mathematical analysis) A vector space over the field of real numbers.
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(algebraic geometry) A morphism between algebraic varieties.
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(linear algebra) A 1×n matrix that represents a vector.
adj
(graph theory, of a graph) Such that there exists a finite vertex set so that for any vertex there exists another vertex in that finite set and an injective homomorphism of the graph that maps the second vertex to the first vertex.
adj
(mathematics) Describing any algebraic system in which only real roots are investigated.
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(algebraic geometry) Having a positive multiple that is generated by global sections.
adj
(algebra) Of a module _RM: such that, for every M→N epimorphism, where N≠0, the socle of N is essential in N.
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(mathematics) A form of partial algebra in category theory.
adj
(mathematics) Of a ring: hereditary for finitely generated submodules.
adj
(algebra, of a ring) Being a commutative reduced ring in which, whenever x, y satisfy x³=y², there is s with s²=x and s³=y.
adj
(mathematics, of a Lie algebra) Being a direct sum of simple Lie algebras.
adj
(linear algebra) Of a matrix, satisfying A^( textsf )T=-A, i.e. having entries on one side of the diagonal that are the additive inverses of their correspondents on the other side of the diagonal and having only zeroes on the main diagonal.
adj
(mathematics) Describing a Boolean algebra in which each subalgebra is atomic.
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(mathematics) A form of supermatrix in gauge mathematics
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(mathematics, physics) A linear operator acting on a space of linear operators
adj
(mathematics) Describing a group whose every injective cellular automaton is surjective
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(mathematics) A group whose elements are precisely all of the bijections of some set with itself and whose operation is composition of those bijections.
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algebraic geometry An algebraic variety equipped a group action of an algebraic torus.
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(mathematics) A principal homogeneous space for a group, such that the stabilizer subgroup of any point is trivial.
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(mathematics) a function mapping a subset of ℝⁿ into a subset of ℝⁿ
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(mathematics) An element of the group algebra of the symmetric group, constructed in such a way that, for the homomorphism from the group algebra to the endomorphisms of a vector space V^(⊗n) obtained from the action of S_n on V^(⊗n) by permutation of indices, the image of the endomorphism determined by that element corresponds to an irreducible representation of the symmetric group over the complex numbers.
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(mathematics) A generalization of a De Morgan algebra that defines a boolean algebra using only implication and a constant.
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