These papers considered a special class of C *- algebras which are now known as von Neumann algebras.

These lead naturally to the definition of C *- algebras and other operator algebras.

Note: These models refer to Lie algebras not to Lie groups.

* Linear algebraic groups ( or more generally affine group schemes ) — These are the analogues of Lie groups, but over more general fields than just R or C. Although linear algebraic groups have a classification that is very similar to that of Lie groups, and give rise to the same families of Lie algebras, their representations are rather different ( and much less well understood ).

These more general algebras are usually called structures, and they are studied in model theory and in theoretical computer science.

These were originally proved by considering Boolean algebras and applying Stone duality.

These algebras all have an involution ( or conjugate ), with the product of an element and its conjugate ( or sometimes the square root of this ) called the norm.

These unital zero algebras may be more generally useful, as they allow to translate any general property of the algebras to properties of vector spaces or modules.

These algebras also carry a topology ; many of them are defined on an underlying Banach space, which turns them into Banach algebras.

These noncommutative algebras, and the non-associative Lie algebras, were studied within universal algebra before the subject was divided into particular mathematical structure types.

These algebras are the objects of a category, with R-algebra homomorphisms as morphisms.

These exceptional groups were discovered around 1890 in the classification of the simple Lie algebras, over the complex numbers ( Wilhelm Killing, re-done by Élie Cartan ).

SU ( m / n ) These are the superunitary Lie algebras which have invariants:

These included number theory, algebras with involution, mathematical analysis, differential geometry and classical mechanics.

These include C *- algebras and von Neumann algebras.

These algebras include certain quotients of the group algebras of braid groups.

These sequences corresponds to sequences in Clifford algebras – see classification of Clifford algebras ; over the complex numbers:

These lectures formed the nucleus of a general survey of English development which took form afterward as A History Of England.

These principles, however, will not be served by violence in any form.

These conceptions and the manner in which they were transposed into poetry or engendered by poetic form are intrinsic to western life from the time of Aeschylus to that of Shakespeare.

These two pieces of information for each dictionary form that is matched by a text form constitute the table of dictionary usage.

These two recollections form the frame around a series of experiences and sights which, to me at least, symbolize the extremes in the aesthetic as well as ethical conflict between materialism and humanism.

These theoretical relationships are more clearly illustrated in Fig. 7 and their sum can be seen to correlate in form with practical measurements made with the Hesiometer as illustrated in the first portion of Fig. 5 for the cutting mechanism.

These oils develop hard, smooth films when they dry and form resinlike substances.

These time scales are denoted in the form UTC ( NPL ) in the UTC form, where NPL in this case identifies the National Physical Laboratory, UK.

These protists live as individual amoebae until starved, at which point they aggregate and form a multicellular fruiting body in which some cells sacrifice themselves to promote the survival of other cells in the fruiting body.

These free-standing statues were usually marble, but also the form rendered in limestone, bronze, ivory and terracotta.

These form thirteen established families ( plus perhaps Shompen, which is poorly attested, as a fourteenth ), which have traditionally been grouped into two, as Mon – Khmer and Munda.

These are long, cylindrical, limbless animals with a snake or worm-like form.

These provinces may take the form of national churches ( such as in Canada, Uganda, or Japan ) or a collection of nations ( such as the West Indies, Central Africa, or Southeast Asia ).

These holes collectively make up what is known as the selenizone which form as the shell grows.

Galileo announced his discovery that Venus had phases like the Moon in the form " Haec immatura a me iam frustra leguntur-oy " ( Latin: These immature ones have already been read in vain by me-oy ), that is, when rearranged, " Cynthiae figuras aemulatur Mater Amorum " ( Latin: The Mother of Loves Venus imitates the figures of Cynthia the moon ).

These early human cultures later interpreted these spirits to be present in animals, the living plant world, and even in natural objects in a form of animism.

These experiments also led to a number of patents: for example, he invented a new form of laminated bent-plywood furniture in 1932.

These illuminations were applied to other works besides the Quran, and it became a respected art form in and of itself.

These early Japanese lamellar armours took the form of a sleeveless jacket and a helmet.

These points form a line, and y = x is said to be the equation for this line.

These form the following five taxonomic groups:

These guitars are most commonly used by swing and jazz players and often incorporate electronics in the form of a pickup.

These realities form a " composite faithfulness " and are ( i ) " perseverance in the apostolic doctrine "; ( ii ) " the will to proclaim God's word "; ( iii ) " communion in the fundamental continuity of the Church, the Body of Christ, the faithful celebration of Baptism and the Eucharist "; ( iv ) " succession in the laying on of hands, the sign of ministerial continuity ".

These states are unified by the fact that their behavior is described by a wave equation or some generalization thereof.

These two directions of generalization can be combined in the inverse function theorem for Banach manifolds.

These scientists pursued several avenues of generalization, including extending the foundations of geometry and adding an extra spatial dimension.

These energy levels can be calculated with reasonable accuracy using the Einstein – Brillouin – Keller method, which is also the basis of the Bohr model of atomic hydrogen .< ref name =" knudson_2006 " >< ref name =" strand_1979 " > More recently, as explained further in the quantum-mechanical version, analytical solutions to the eigenenergies have been obtained: these are a generalization of the Lambert W function.

These operations are generalization of crisp set operations.