Automorphism group and dimension of ordered sets

It is shown that a finite groupG is isomorphic to the automorphism group of a two-dimensional ordered set if and only if it is a generalized wreath product of symmetric groups over an ordered index set that is a dual tree. Furthermore, every finite abelian group is isomorphic to the full automorphism group of a three-dimensional ordered set. Also every finite group is isomorphic to the automorphism group of an ordered set that does not contain an induced crown with more than four elements.     

Automorphism group actions in complex analysis

In this paper we describe the subject of automorphism groups of domains in complex space. This has been an active area of research for fifty years or more, and continues to be dynamic and developing today. We discuss noncompact automorphism groups, the Bun Wong/Rosay theorem, the Greene/Krantz conjecture, semicontinuity of automorphism groups, the method of scaling, and other current topics. Contributions from geometers, Lie theorists, analysts, and function theorists are described.     

Automorphism group of exceptional symmetric domainsR V

The exceptional symmetric Siegel domainR _v(16) in ?¹⁶ is defined. The exceptional classical domain ?_v(16) = t(R_v(16)) is computed, where t is the Bergman mapping of the Siegel domain R_v(16). And holomorphical automorphism group Aut (R_v(16)) of the exceptional symmetric Siegel domainR _v(16) is presented     

Automorphism group of exceptional symmetric domains RVI

Here we give the definition of the exceptional symmetric Siegel domain R_VI(27) in C²⁷, and compute the exceptional symmetric domain ?_VI(27) = τ(R_VI(27)), where t is the Bergman mapping of the Siegel domainR _VI (27). Moreover, we present the holomorphical automorphism group Aut (?_VI(27)) of the exceptional symmetric domain (?_VI(27)).     

Automorphism group of exceptional symmetric domains RV

The exceptional symmetric Siegel domain RV(16) in C16 is defined. The exceptional classical domain (R)v(16)=τ(RV(16)) is computed, where τ is the Bergman mapping of the Siegel domain RV(16). And holomorphical automorphism group Aut (RV(16)) of the exceptional symmetric Siegel domain RV(16) is presented.     

Automorphism group and representation of a twisted multi-loop algebra

Let G be the complexification of the real Lie algebra so（3） and A = C[t1^±1, t2^±1] be the Lau-ent polynomial algebra with commuting variables. Let L：（t1, t2, 1） = G c .A be the twisted multi-loop Lie algebra. Recently we have studied the universal central extension, derivations and its vertex operator representations. In the present paper we study the automorphism group and bosonic representations ofL（t1, t2, 1）.     

Automorphism group of exceptional symmetric domains RVI

Here we give the definition of the exceptional symmetric Siegel domain R_VI(27) in C²⁷, and compute the exceptional symmetric domain ℛ_VI(27) = τ(R_VI(27)), where t is the Bergman mapping of the Siegel domainR _VI (27). Moreover, we present the holomorphical automorphism group Aut (ℛ_VI(27)) of the exceptional symmetric domain (ℛ_VI(27)).     

Automorphism group of Green ring of Sweedler Hopf algebra

Let H ₂ be Sweedler’s 4-dimensional Hopf algebra and r(H ₂) be the corresponding Green ring of H ₂. In this paper, we investigate the automorphism groups of Green ring r(H ₂) and Green algebra F(H ₂) = r(H ₂)?_? F, where F is a field, whose characteristics is not equal to 2. We prove that the automorphism group of r(H ₂) is isomorphic to K ₄, where K ₄ is the Klein group, and the automorphism group of F(H ₂) is the semidirect product of ?₂ and G, where G = F {1/2} with multiplication given by a · b = 1? a ? b + 2ab.     

Automorphism groups of posets and lattices with a given subset of fixed points

For a posetP, let Aut (P) denote the automorphism group ofP and let Fp (P) be the subposet of all fixed points of Aut (P). It is shown that for every posetP and every nontrivial groupG the posetsP satisfying Aut (P)G and Fp(P)=P form a proper class.Similarly, for a latticeL, let Aut (L) denote the automorphism group and Fp(L) the sublattice of fixed points. It is shown that ifL has more than one element andG is a nontrivial group then the latticesL for which Aut (L)G and Fp(L)=L also form a proper class. Moreover, if card (L)1 then this is still the case providingG is an infinite group. Since card (L)2 when Aut (L) is finite, this is the best possible result.With 3 FiguresThe support of the National Research Council of Canada is gratefully acknowledged.