7 citations · 9 across the 14 of their papers we have counts for
20 papers
Constructing solvable groups whose character degree graphs generalize the bowtie
Jacob Laubacher, Mark L. Lewis, Lorenzo Ravaglia +1
We present here a generalized construction of a finite solvable group whose prime character degree graph has the shape and structure of the bowtie graph. As with the original bowti…
Splitting fields and spectral invariants of character degree graphs in solvable groups
G. Sivanesan, C. Selvaraj, Jacob Laubacher
In this paper, we investigate the eigenvalues of character degree graphs, with particular emphasis on the arithmetic properties of their spectra. First, we study \((n-2)\)-regular…
On prime character degree graphs occurring within a family of graphs (iii)
Mark W. Bissler, Thatcher Debowski, Theodore F. Hoelker +3
We conclude the classification work done in the two previous papers of the same name. Here we add flexibility to the construction, thereby viewing the graphs in full generality. Ou…
Properties of reproducing kernel Hilbert spaces of a group action
Tyler Blom, Samuel A. Hokamp, Alejandro Jimenez +1
In this paper, we investigate properties of a reproducing kernel Hilbert space of a group action. In particular, we introduce an equivalence relation on a compact Hausdorff space $…
On the metric dimension of the character degree graph of a solvable group
Peter J. Cameron, G. Sivanesan, C. Selvaraj +2
Let be a finite solvable group and let be the character degree graph of . In this paper, we obtain the metric dimension of certain character degree graphs. Specifical…
Replacing bar-like resolutions in a simplicial setting
Samuel Carolus, Jacob Laubacher, Sydney D. Vitalbo +1
It is well known that the bar resolution can be replaced with any projective resolution of the corresponding algebra when computing the Hochschild (co)homology of that algebra. Thi…
Classifying character degree graphs with seven vertices
Jacob Laubacher, Mark Medwid, Dylan Schuster
We study here the graphs with seven vertices in an effort to classify which of them appear as the prime character degree graphs of finite solvable groups. This classification is co…
Secondary Hochschild cohomology and derivations
Kylie Bennett, Elizabeth Heil, Jacob Laubacher
In this paper, we introduce a generalization of derivations. Using these so-called secondary derivations, along with an analogue of Connes' Long Exact Sequence, we are able to prov…
Secondary Hochschild homology and differentials
Jacob Laubacher
In this paper we study a generalization of Kähler differentials, which correspond to the secondary Hochschild homology associated to a triple . We establish comp…
On prime character degree graphs occurring within a family of graphs (ii)
Sara DeGroot, Jacob Laubacher, Mark Medwid
In this paper, we continue the classification work done in the first paper of the same name. With careful modifications of our previous approach, we are able to deduce (with two no…
On prime character degree graphs occurring within a family of graphs
Jacob Laubacher, Mark Medwid
In this paper we investigate families of connected graphs which do not contain an odd cycle in their complement. Specifically, we consider graphs formed by two complete graphs conn…
Deformation Theories Controlled by Hochschild Cohomologies
Samuel Carolus, Samuel A. Hokamp, Jacob Laubacher
We explore how the higher order Hochschild cohomology controls a deformation theory when the simplicial set models the 3-sphere. Besides generalizing to the -sphere for any $d\g…
A Simplicial Construction for Noncommutative Settings
Samuel Carolus, Jacob Laubacher, Mihai D. Staic
In this paper we present a general construction that can be used to define the higher Hochschild homology for a noncommutative algebra. We also discuss other examples where this co…
On the Absence of a Normal Nonabelian Sylow Subgroup
Mark W. Bissler, Jacob Laubacher, Corey F. Lyons
Let be a finite solvable group. We show that does not have a normal nonabelian Sylow -subgroup when its prime character degree graph satisfies a technical hypothe…
Classifying Character Degree Graphs With 6 Vertices
Mark W. Bissler, Jacob Laubacher, Mark L. Lewis
We investigate prime character degree graphs of solvable groups that have six vertices. There are one hundred twelve non-isomorphic connected graphs with six vertices, of which all…
Classifying Families of Character Degree Graphs of Solvable Groups
Mark W. Bissler, Jacob Laubacher
We investigate prime character degree graphs of solvable groups. In particular, we consider a family of graphs constructed by adjoining edges between two complete graphs…
Simplicial Structures Over the 3-Sphere and Generalized Higher Order Hochschild Homology
Samuel Carolus, Jacob Laubacher
In this paper we investigate the simplicial structure of a chain complex associated to the higher order Hochschild homology over the -sphere. We also introduce the tertiary Hoch…
A family of graphs that cannot occur as character degree graphs of solvable groups
Mark W. Bissler, Jacob Laubacher, Mark L. Lewis
We investigate character degree graphs of solvable groups. In particular, we provide general results that can be used to eliminate which degree graphs can occur as solvable groups.…
Properties of the Secondary Hochschild Homology
Jacob Laubacher
In this paper we study properties of the secondary Hochschild homology of the triple with coefficients in . We establish a type of Morita equivalence between…
Bar Simplicial Modules and Secondary Cyclic (Co)homology
Jacob Laubacher, Mihai D. Staic, Alin Stancu
In this paper we study the simplicial structure of the complex , associated to the secondary Hochschild cohomology. The main ingredient is the si…