### Some articles on *automorphisms*:

Steenrod Algebra - Relation To Formal Groups

... These group schemes are closely related to the

... These group schemes are closely related to the

**automorphisms**of 1-dimensional additive formal groups ... Steenrod algebra is the group scheme of**automorphisms**of the 1-dimensional additive formal group scheme x+y that are the identity to first order ... These**automorphisms**are of the form ...Homogeneous Space - Formal Definition

... Note that automatically G acts by

... Note that automatically G acts by

**automorphisms**(bijections) on the set ... to some category, then the elements of G are assumed to act as**automorphisms**in the same category ... into the group of**automorphisms**of the object X in the category C ...Moduli Of Algebraic Curves - Moduli Stacks of Stable Curves

... no singularities other than double points, and has only a finite group of

... no singularities other than double points, and has only a finite group of

**automorphisms**... In lower genus, one must account for the presence of smooth families of**automorphisms**, by subtracting their number ... the dimension of is dim(space of genus zero curves) - dim(group of**automorphisms**) = 0 - dim(PGL(2)) = -3 ...Tomita–Takesaki Theory - KMS States

... A KMS state φ on a von Neumann algebra M with a given 1-parameter group of

... A KMS state φ on a von Neumann algebra M with a given 1-parameter group of

**automorphisms**αt is a state fixed by the**automorphisms**such that for every pair of elements A, B of M there is a bounded continuous ... Moreover this characterizes the modular**automorphisms**of φ ... to be 1 by rescaling the 1-parameter family of**automorphisms**.) ...**Automorphisms**Of The Symmetric And Alternating Groups

... In group theory, a branch of mathematics, the

**automorphisms**and outer

**automorphisms**of the symmetric groups and alternating groups are both standard examples of these

**automorphisms**...

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