Lie group–Lie algebra correspondenceIn mathematics, Lie group–Lie algebra correspondence allows one to correspond a Lie group to a Lie algebra or vice versa, and study the conditions for such a relationship. Lie groups that are isomorphic to each other have Lie algebras that are isomorphic to each other, but the converse is not necessarily true. One obvious counterexample is and (see real coordinate space and the circle group respectively) which are non-isomorphic to each other as Lie groups but their Lie algebras are isomorphic to each other.
Chirality (physics)A chiral phenomenon is one that is not identical to its (see the article on mathematical chirality). The spin of a particle may be used to define a handedness, or helicity, for that particle, which, in the case of a massless particle, is the same as chirality. A symmetry transformation between the two is called parity transformation. Invariance under parity transformation by a Dirac fermion is called chiral symmetry. Helicity (particle physics) The helicity of a particle is positive (“right-handed”) if the direction of its spin is the same as the direction of its motion.
One-parameter groupIn mathematics, a one-parameter group or one-parameter subgroup usually means a continuous group homomorphism from the real line (as an additive group) to some other topological group . If is injective then , the image, will be a subgroup of that is isomorphic to as an additive group. One-parameter groups were introduced by Sophus Lie in 1893 to define infinitesimal transformations. According to Lie, an infinitesimal transformation is an infinitely small transformation of the one-parameter group that it generates.
Construction estimating softwareConstruction cost estimating software is computer software designed for contractors to estimate construction costs for a specific project. A cost estimator will typically use estimating software to estimate their bid price for a project, which will ultimately become part of a resulting construction contract. Some architects, engineers, construction managers, and others may also use cost estimating software to prepare cost estimates for purposes other than bidding such as budgeting and insurance claims.
Galois theoryIn mathematics, Galois theory, originally introduced by Évariste Galois, provides a connection between field theory and group theory. This connection, the fundamental theorem of Galois theory, allows reducing certain problems in field theory to group theory, which makes them simpler and easier to understand. Galois introduced the subject for studying roots of polynomials.
