* Sp ( n ) and Sp ( 2n, F ), a term used in mathematics to denote a symplectic group or its corresponding Lie algebra

The same term is also used for other Hopf algebras that deform or are close to classical Lie groups or Lie algebras, such as a ` bicrossproduct ' class of quantum groups introduced by Shahn Majid a little after the work of Drinfeld and Jimbo.

With this in mind, the term discrete group theory is used to refer to the study of groups without topological structure, in contradistinction to topological or Lie group theory.

Outside of Lie theory, the term fundamental representation is sometimes loosely used to refer to a smallest-dimensional faithful representation, though this is also often called the standard or defining representation ( a term referring more to the history, rather than having a well-defined mathematical meaning ).

The term " Lie algebra " was introduced in 1934 by Hermann Weyl, for what had until then been known as the algebra of infinitesimal transformations of a Lie group.

* Lie ( obstetrics ), an obstetrical term for the axis of the foetus

Drinfeld coined the term " Quantum group " in reference to Hopf algebras, which are deformations of simple Lie algebras, and connected them to the study of the Yang – Baxter equation, which is a necessary condition for the solvability of statistical mechanical models.

However, in his 1986 book Applications of Lie Groups to Differential Equations ( p. 127 ) he uses the term " hyperbolic rotation " for an equivalent mapping.

* SO ( 10 ) ( physics ), a term used in particle physics, one of the grand unified theories is based on the SO ( 10 ) Lie group

In the longer term, it has not been the direct application of continuous symmetry to geometric questions that has made Lie theory a central chapter of contemporary mathematics.

Clockwise from top left: Kielland, Lie, Ibsen, and Bjørnson. The Four Greats ( in Danish and Norwegian De Fire Store ) is a term used for four of the most influential Norwegian writers of the late 19th century, namely Bjørnstjerne Bjørnson, Henrik Ibsen, Alexander Kielland and Jonas Lie.

As it is now known that all B *- algebras are C *- algebras ( and vice versa ), the term B *- algebra is no longer widely used.

Because of this, the term B * algebra is rarely used in current terminology, and has been replaced by the ( overloading of ) the term ' C * algebra '.

For these reasons, the term-algebra is rarely used in current terminology, and has been replaced by the term ' algebra '.

In particular, the term " graph " was introduced by Sylvester in a paper published in 1878 in Nature, where he draws an analogy between " quantic invariants " and " co-variants " of algebra and molecular diagrams:

The term was introduced by Benjamin Peirce in the context of elements of an algebra that remain invariant when raised to a positive integer power, and literally means "( the quality of having ) the same power ", from idem + potence ( same + power ).

In Alfred North Whitehead's book A Treatise on Universal Algebra, published in 1898, the term universal algebra had essentially the same meaning that it has today.

" At the time George Boole's algebra of logic made a strong counterpoint to ordinary number algebra, so the term " universal " served to calm strained sensibilities.

Algebra was significantly developed by Persian scientist Muhammad ibn Mūsā al-Khwārizmī during this time in his landmark text, Kitab al-Jabr wa-l-Muqabala, from which the term algebra is derived.

The term " sedenion " is also used for other 16-dimensional algebraic structures, such as a tensor product of 2 copies of the quaternions, or the algebra of 4 by 4 matrices over the reals, or that studied by.

In mathematics, a hypercomplex number is a traditional term for an element of an algebra over a field where the field is the real numbers or the complex numbers.

From that date the preferred term for a hypercomplex system became associative algebra as seen in the title of Wedderburn ’ s thesis at University of Edinburgh.

Notable special usages of the term include the concepts of complete Boolean algebra, complete lattice, and complete partial order ( cpo ).

Eight years after John McCarthy coined the term artificial intelligence, Bobrow's dissertation ( titled Natural Language Input for a Computer Problem Solving System ) showed how a computer can understand simple natural language input to solve algebra word problems.

* A superalgebra is another term for a Z < sub > 2 </ sub >- graded algebra.

The term generic programming was originally coined by David Musser and Alexander Stepanov in a more specific sense than the above, to describe an approach to software decomposition whereby fundamental requirements on types are abstracted from across concrete examples of algorithms and data structures and formalised as concepts, analogously to the abstraction of algebraic theories in abstract algebra.

In mathematics, and more specifically abstract algebra, the term algebraic structure generally refers to an arbitrary set ( called carrier set or underlying set ) with one or more finitary operations defined on it.

An algebraic structure in a variety may be understood as the quotient algebra of term algebra ( also called " absolutely free algebra ") divided by the equivalence relations generated by a set of identities.

So, a collection of functions with given signatures generate a free algebra, the term algebra T. Given a set of equational identities ( the axioms ), one may consider their symmetric, transitive closure E. The quotient algebra T / E is then the algebraic structure or variety.

The Latin synonym is " sonic ", after which the term sonics used to be a synonym for acoustics and later a branch of acoustics.

As a result, after serving a single term, he was defeated for re-election.

However, the term came into wide use only after the publication of a review article by O. Jacobsen in the chemical dictionary of Albert Ladenburg in the 1880s.

The Social Democratic Party ( SPD ) and The Left ( Die Linke ) took control of the city government after the 2001 state election and won another term in the 2006 state election.

Until 1928 it was directed by a General Manager, after this time instead by a Governor elected by an internal commission of managers, with a decree from the President of the Italian Republic for a term of 7 years.

This number can be seen as equal to the one of the first definition, independently of any of the formulas below to compute it: if in each of the n factors of the power one temporarily labels the term X with an index i ( running from 1 to n ), then each subset of k indices gives after expansion a contribution X < sup > k </ sup >, and the coefficient of that monomial in the result will be the number of such subsets.

Long-term use is controversial due to concerns about adverse psychological and physical effects, increased questioning of effectiveness and because benzodiazepines are prone to cause tolerance, physical dependence, and, upon cessation of use after long term use, a withdrawal syndrome.

Discontinuation after long term use in epilepsy requires additional caution because of the risks of rebound seizures.

From 1907 on, English language articles sometimes used the term " Maximalist " for " Bolshevik " and " Minimalist " for " Menshevik ", which proved confusing since there was also a " Maximalist " faction within the Russian Socialist-Revolutionary Party in 1904 – 1906 ( which after 1906 formed a separate Union of Socialists-Revolutionaries Maximalists ) and then again after 1917.

* According to culinary writer Giuliano Bugialli, the term comes from the Italian bagno maria, named after Maria de ' Cleofa, who developed the technique in Florence in the sixteenth century.

In the United States, the term for most existing works is a fixed number of years after the date of creation or publication.

The term clade was introduced in 1958 by Julian Huxley after having been coined by Lucien Cuénot in 1940, cladistic by Cain and Harrison in 1960, and cladist ( for an adherent of Hennig's school ) by Mayr in 1965.

Shortly after, in 1869, Irish chemist Thomas Andrews studied the phase transition from a liquid to a gas and coined the term critical point to describe the instant at which a gas and a liquid were indistinguishable as phases, and Dutch physicist Johannes van der Waals supplied the theoretical framework which allowed the prediction of critical behavior based on measurements at much higher temperatures.

On April 14, after its first session, the PRA announced that Khieu Samphan would chair the State Presidium for a 5-year term.

A constitutional amendment approved in 1969 limits presidents and deputies to one term, although a deputy may run again for an Assembly seat after sitting out a term.

Eunuch is a more general term, since historically many eunuchs were castrated after puberty, castration thus having no effect on their voices.

Caltech is on the quarter system: the fall term starts in late September and ends before Christmas, the second term starts after New Years Day and ends in mid-March, and the third term starts in late March or early April and ends in early June.

Only in the time before Hugh Capet took the crown for himself and after the reign of Charles X is the term necessary to identify which.

Puerto Rican comedian and entrepreneur Silverio Pérez is credited with coining the term chupacabras soon after the first incidents were reported in the press.

Though conquerors, the Chaldeans were rapidly and completely assimilated into the dominant Babylonian culture, as the Amorites before them had been, and after the fall of Babylon in 539 BC the term " Chaldean " was no longer used to describe a specific race of people, but rather a " socio-Economic " class, regardless of ethnicity.

In a historical or geopolitical sense the term usually refers collectively to Christian majority countries or countries in which Christianity dominates or was a territorial phenomenon .“ Christendom is originally a medieval concept steadily to have evolved since the fall of the Western Roman Empire and the gradual rise of the Papacy more in religio-temporal implication practically during and after the reign of Charlemagne ; and the concept let itself to be lulled in the minds of the staunch believers to the archetype of a holy religious space inhabited by Christians, blessed by God, the Heavenly Father, ruled by Christ through the Church and protected by the Spirit-body of Christ ; no wonder, this concept, as included the whole of Europe and then the expanding Christian territories on earth, strengthened the roots of Romance of the greatness of Christianity in the world .”