X-Nico

3 unusual facts about Approximately finite dimensional C*-algebra


Approximately finite dimensional C*-algebra

Approximate finite dimensionality was first defined and described combinatorially by Bratteli.

The counterpart of simple AF C*-algebras in the von Neumann algebra world are the hyperfinite factors, which were classified by Connes and Haagerup.

Connes obtained the analogous result for the II factor.


Affiliated operator

Later Atiyah and Singer showed that index theorems for elliptic operators on closed manifolds with infinite fundamental group could naturally be phrased in terms of unbounded operators affiliated with the von Neumann algebra of the group.

Banach measure

In mathematics, Banach measure in measure theory may mean a real-valued function on an algebra of all subsets of a set (for example, all subsets of the plane), by means of which a rigid, finitely additive area can be defined for every set, even when a set does not have a true geometric area.

C*-algebra

This line of research began with Werner Heisenberg's matrix mechanics and in a more mathematically developed form with Pascual Jordan around 1933.

Carus Mathematical Monographs

# Algebra and Tiling: Homomorphisms in the Service of Geometry, by Sherman Stein and Sándor Szabó

Charles Haldeman

He then moved to Athens, Greece, where he taught high school biology and algebra at the American Community Schools for two years.

Dublin School

Courses include chemistry, biology, marine biology, algebra, pre-calculus, calculus, statistics, Spanish, French, Latin, Mandarin, world history, American history, economics and English, various AP courses, and various electives in each category.

Duffin–Kemmer–Petiau algebra

In mathematical physics, the Duffin–Kemmer–Petiau algebra (DKP algebra), introduced by R.J. Duffin, Nicholas Kemmer and G. Petiau, is the algebra which is generated by the Duffin–Kemmer–Petiau matrices.

Going up

Going up and going down, terms in commutative algebra which refer to certain properties of chains of prime ideals in integral extensions

Hilbert's theorem

Hilbert's basis theorem, in commutative algebra, stating every ideal in the ring of multivariate polynomials over a Noetherian ring is finitely generated

Hilbert's syzygy theorem, a result of commutative algebra in connection with the syzygy problem of invariant theory

Hilbert's Nullstellensatz, the basis of abstract algebra, establishing a fundamental relationship between geometry and algebra

Hyperbolic sector

The analogy between circular and hyperbolic functions was described by Augustus De Morgan in his Trigonometry and Double Algebra (1849).

Iwahori–Hecke algebra

In mathematics, the Iwahori–Hecke algebra, or Hecke algebra, named for Erich Hecke and Nagayoshi Iwahori, is a one-parameter deformation of the group algebra of a Coxeter group.

Jamal Nebez

In 1956, he prepared a stencilized script on Algebra and in 1960, succeeded in publishing the first physics book in Kurdish under the title, "Introduction into the Mechanics and Properties of Matter", including a rich glossary of Kurdish terms pertaining to physics and mathematics.

Joachim Cuntz

Joachim Cuntz is known for his contributions regarding the theory of operator and in the field of the non-commutative geometry, with particular contributions to the structure of simple C*-algebras, the K-theory and cyclic homology.

Johannes Nikolaus Tetens

His interest in polynomial algebra was influenced by his belonging to the German combinatorial school of Carl Friederich Hindenburg, Christian Kramp and others.

K shortest path routing

In 2010, Michael Gunter et al. published a book on Symbolic calculation of K-shortest paths and related measures with the stochastic process algebra tool CASPA.

Kac–Moody algebra

In mathematics, a Kac–Moody algebra (named for Victor Kac and Robert Moody, who independently discovered them) is a Lie algebra, usually infinite-dimensional, that can be defined by generators and relations through a generalized Cartan matrix.

Karen Parshall

with Jeremy J. Gray (eds.): Episodes in the History of Modern Algebra (1800–1950), AMS/LMS History of Mathematics 32, Providence/London 2007 (Conference at MSRI 2003)

King Henry VIII School Abergavenny

The school at this time was supposed to be a grammar school taking pupils from all over North Monmouthshire with a curriculum of Latin, English, History, Geography, French, Arithmetic, Algebra, Trigonometry and Chemistry.

KK-theory

It was influenced by Atiyah's concept of Fredholm modules for the Atiyah–Singer index theorem, and the classification of extensions of C*-algebras by Brown–Douglas–Fillmore (Lawrence G. Brown, Ronald G. Douglas, Peter Arthur Fillmore 1977).

Levi decomposition

Analogous statements hold for simply connected Lie groups, and, as shown by George Mostow, for algebraic Lie algebras and simply connected algebraic groups over a field of characteristic zero.

Lie-* algebra

In mathematics, a Lie-* algebra is a D-module with a Lie* bracket.

M-sequence

Regular sequence, which is an important topic in commutative algebra.

Map algebra

Map algebra is a set-based algebra for manipulating geographic data, proposed by Dr. Dana Tomlin in the early 1980s.

Merkuryev

Alexander Merkurjev (born 1955) is a Russian-born American mathematician, who has made major contributions to the field of algebra;

Multilateration

There are many robust linear algebra methods that can solve for the values of (x,y,z), such as Gaussian Elimination.

N! conjecture

It was Adriano Garsia's idea to construct an appropriate module in order to prove positivity (as was done in his previous joint work with Procesi on Schur positivity of Kostka–Foulkes polynomials).

Narrative

Narratives can be both abstracted and generalised by imposing an algebra upon their structures and thence defining homomorphism between the algebras.

Newton's method

Newton's method was first published in 1685 in A Treatise of Algebra both Historical and Practical by John Wallis.

Normal matrix

The concept of normal matrices can be extended to normal operators on infinite dimensional Hilbert spaces and to normal elements in C*-algebras.

Philip Palmer Green

He earned his doctorate from Berkeley in mathematics in 1976 with a dissertation on C*-algebra, but, like his colleague Eric Lander, transitioned from pure mathematics into applied work in biology and bioinformatics.

Physical symbol system

Algebra: the symbols are "+", "×", "x", "y", "1", "2", "3", etc.

Pp-wave spacetime

A more general subclass consists of the axisymmetric pp-waves, which in general have a two dimensional Abelian Lie algebra of Killing vector fields.

Quillen–Suslin theorem

Leonid Vaseršteĭn later gave a simpler and much shorter proof of the theorem which can be found in Serge Lang's Algebra.

Regina Tyshkevich

An international conference "Discrete Mathematics, Algebra, and their Applications", sponsored by the Central European Initiative, was held in Minsk, Belarus, October 2009 in honor of her 80th birthday.

Rigid analytic space

Vladimir Berkovich reformulated much of the theory of rigid analytic spaces in the late 1980s, using a generalization of the notion of Gelfand spectrum for commutative unital C*-algebras.

Risch algorithm

The Risch algorithm is summarized (in more than 100 pages) in Algorithms for Computer Algebra by Keith O. Geddes, Stephen R. Czapor and George Labahn.

Seki Takakazu

Chinese algebra discovered numerical evaluation (Horner's method, re-established by William George Horner in the 19th century) of arbitrary degree algebraic equation with real coefficients.

Semiring

Similarly, the Viterbi algorithm for finding the most probable state sequence corresponding to an observation sequence in a Hidden Markov model can also be formulated as a computation over a (max, ×) algebra on probabilities.

SmallBASIC

SmallBASIC is also intended as a tool for mathematics, with built-in functions for Unit conversion, Algebra, Matrix math, Trigonometry, Statistics, and for two and three dimensional Equation Graphing.

Sol Garfunkel

Sol is best known for hosting the 1987, PBS series titled "For All Practical Purposes: An Introduction to Contemporary Mathematics", followed by the 1991 series, "Algebra: In Simplest Terms", both often used in classrooms.

Spinors in three dimensions

This algebra admits a convenient description, due to William Rowan Hamilton, by means of quaternions.

Splitting circle method

It was introduced by Arnold Schönhage in his 1982 paper The fundamental theorem of algebra in terms of computational complexity (Technical report, Mathematisches Institut der Universität Tübingen).

Theodor Vahlen

His 1902 paper in Mathematische Annalen recounts William Kingdon Clifford's construction of his 2n dimensional algebra with n − 1 anti-commuting square roots of −1.

TICCIT

MITRE subcontracted with the CAI Laboratory at the University of Texas at Austin and also with the Department of Instructional Research, Development, and Evaluation of Brigham Young University to refine the user interface and create the massive amounts of courseware needed to teach a complete college-level English and algebra course.

Zvi Arad

Since 1994 he has served on the editorial board of the Algebra Colloquium, a journal of the Chinese Academy of Sciences published by Springer-Verlag.


see also